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Simplifying (0.0484) + (4x)(x) = 0.10(1.00 + -1x)(0.70 + -1x) 0.0484 + (4x)(x) = 0.10(1.00 + -1x)(0.70 + -1x) Remove parenthesis around (4x) 0.0484 + 4x(x) = 0.10(1.00 + -1x)(0.70 + -1x) Multiply x * x 0.0484 + 4x2 = 0.10(1.00 + -1x)(0.70 + -1x) Multiply (1.00 + -1x) * (0.70 + -1x) 0.0484 + 4x2 = 0.10(1.00(0.70 + -1x) + -1x * (0.70 + -1x)) 0.0484 + 4x2 = 0.10((0.70 * 1.00 + -1x * 1.00) + -1x * (0.70 + -1x)) 0.0484 + 4x2 = 0.10((0.7 + -1x) + -1x * (0.70 + -1x)) 0.0484 + 4x2 = 0.10(0.7 + -1x + (0.70 * -1x + -1x * -1x)) 0.0484 + 4x2 = 0.10(0.7 + -1x + (-0.7x + 1x2)) Combine like terms: -1x + -0.7x = -1.7x 0.0484 + 4x2 = 0.10(0.7 + -1.7x + 1x2) 0.0484 + 4x2 = (0.7 * 0.10 + -1.7x * 0.10 + 1x2 * 0.10) 0.0484 + 4x2 = (0.07 + -0.17x + 0.1x2) Solving 0.0484 + 4x2 = 0.07 + -0.17x + 0.1x2 Solving for variable 'x'. Reorder the terms: 0.0484 + -0.07 + 0.17x + 4x2 + -0.1x2 = 0.07 + -0.17x + 0.1x2 + -0.07 + 0.17x + -0.1x2 Combine like terms: 0.0484 + -0.07 = -0.0216 -0.0216 + 0.17x + 4x2 + -0.1x2 = 0.07 + -0.17x + 0.1x2 + -0.07 + 0.17x + -0.1x2 Combine like terms: 4x2 + -0.1x2 = 3.9x2 -0.0216 + 0.17x + 3.9x2 = 0.07 + -0.17x + 0.1x2 + -0.07 + 0.17x + -0.1x2 Reorder the terms: -0.0216 + 0.17x + 3.9x2 = 0.07 + -0.07 + -0.17x + 0.17x + 0.1x2 + -0.1x2 Combine like terms: 0.07 + -0.07 = 0.00 -0.0216 + 0.17x + 3.9x2 = 0.00 + -0.17x + 0.17x + 0.1x2 + -0.1x2 -0.0216 + 0.17x + 3.9x2 = -0.17x + 0.17x + 0.1x2 + -0.1x2 Combine like terms: -0.17x + 0.17x = 0.00 -0.0216 + 0.17x + 3.9x2 = 0.00 + 0.1x2 + -0.1x2 -0.0216 + 0.17x + 3.9x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -0.0216 + 0.17x + 3.9x2 = 0.0 Begin completing the square. Divide all terms by 3.9 the coefficient of the squared term: Divide each side by '3.9'. -0.005538461538 + 0.04358974359x + x2 = 0 Move the constant term to the right: Add '0.005538461538' to each side of the equation. -0.005538461538 + 0.04358974359x + 0.005538461538 + x2 = 0 + 0.005538461538 Reorder the terms: -0.005538461538 + 0.005538461538 + 0.04358974359x + x2 = 0 + 0.005538461538 Combine like terms: -0.005538461538 + 0.005538461538 = 0.000000000000 0.000000000000 + 0.04358974359x + x2 = 0 + 0.005538461538 0.04358974359x + x2 = 0 + 0.005538461538 Combine like terms: 0 + 0.005538461538 = 0.005538461538 0.04358974359x + x2 = 0.005538461538 The x term is 0.04358974359x. Take half its coefficient (0.0217948718). Square it (0.0004750164368) and add it to both sides. Add '0.0004750164368' to each side of the equation. 0.04358974359x + 0.0004750164368 + x2 = 0.005538461538 + 0.0004750164368 Reorder the terms: 0.0004750164368 + 0.04358974359x + x2 = 0.005538461538 + 0.0004750164368 Combine like terms: 0.005538461538 + 0.0004750164368 = 0.0060134779748 0.0004750164368 + 0.04358974359x + x2 = 0.0060134779748 Factor a perfect square on the left side: (x + 0.0217948718)(x + 0.0217948718) = 0.0060134779748 Calculate the square root of the right side: 0.077546618 Break this problem into two subproblems by setting (x + 0.0217948718) equal to 0.077546618 and -0.077546618.Subproblem 1
x + 0.0217948718 = 0.077546618 Simplifying x + 0.0217948718 = 0.077546618 Reorder the terms: 0.0217948718 + x = 0.077546618 Solving 0.0217948718 + x = 0.077546618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0217948718' to each side of the equation. 0.0217948718 + -0.0217948718 + x = 0.077546618 + -0.0217948718 Combine like terms: 0.0217948718 + -0.0217948718 = 0.0000000000 0.0000000000 + x = 0.077546618 + -0.0217948718 x = 0.077546618 + -0.0217948718 Combine like terms: 0.077546618 + -0.0217948718 = 0.0557517462 x = 0.0557517462 Simplifying x = 0.0557517462Subproblem 2
x + 0.0217948718 = -0.077546618 Simplifying x + 0.0217948718 = -0.077546618 Reorder the terms: 0.0217948718 + x = -0.077546618 Solving 0.0217948718 + x = -0.077546618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0217948718' to each side of the equation. 0.0217948718 + -0.0217948718 + x = -0.077546618 + -0.0217948718 Combine like terms: 0.0217948718 + -0.0217948718 = 0.0000000000 0.0000000000 + x = -0.077546618 + -0.0217948718 x = -0.077546618 + -0.0217948718 Combine like terms: -0.077546618 + -0.0217948718 = -0.0993414898 x = -0.0993414898 Simplifying x = -0.0993414898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0557517462, -0.0993414898}
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