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Simplifying ((0.3 + -1x)(0.3 + -1x)) = 0.2x(0.2 + x) Multiply (0.3 + -1x) * (0.3 + -1x) ((0.3(0.3 + -1x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x) (((0.3 * 0.3 + -1x * 0.3) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x) (((0.09 + -0.3x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x) ((0.09 + -0.3x + (0.3 * -1x + -1x * -1x))) = 0.2x(0.2 + x) ((0.09 + -0.3x + (-0.3x + 1x2))) = 0.2x(0.2 + x) Combine like terms: -0.3x + -0.3x = -0.6x ((0.09 + -0.6x + 1x2)) = 0.2x(0.2 + x) (0.09 + -0.6x + 1x2) = 0.2x(0.2 + x) Remove parenthesis around (0.09 + -0.6x + 1x2) 0.09 + -0.6x + 1x2 = 0.2x(0.2 + x) 0.09 + -0.6x + 1x2 = (0.2 * 0.2x + x * 0.2x) 0.09 + -0.6x + 1x2 = (0.04x + 0.2x2) Solving 0.09 + -0.6x + 1x2 = 0.04x + 0.2x2 Solving for variable 'x'. Reorder the terms: 0.09 + -0.6x + -0.04x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2 Combine like terms: -0.6x + -0.04x = -0.64x 0.09 + -0.64x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2 Combine like terms: 1x2 + -0.2x2 = 0.8x2 0.09 + -0.64x + 0.8x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2 Reorder the terms: 0.09 + -0.64x + 0.8x2 = 0.04x + -0.04x + 0.2x2 + -0.2x2 Combine like terms: 0.04x + -0.04x = 0.00 0.09 + -0.64x + 0.8x2 = 0.00 + 0.2x2 + -0.2x2 0.09 + -0.64x + 0.8x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 0.09 + -0.64x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 0.1125 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.1125' to each side of the equation. 0.1125 + -0.8x + -0.1125 + x2 = 0 + -0.1125 Reorder the terms: 0.1125 + -0.1125 + -0.8x + x2 = 0 + -0.1125 Combine like terms: 0.1125 + -0.1125 = 0.0000 0.0000 + -0.8x + x2 = 0 + -0.1125 -0.8x + x2 = 0 + -0.1125 Combine like terms: 0 + -0.1125 = -0.1125 -0.8x + x2 = -0.1125 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.1125 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.1125 + 0.16 Combine like terms: -0.1125 + 0.16 = 0.0475 0.16 + -0.8x + x2 = 0.0475 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.0475 Calculate the square root of the right side: 0.217944947 Break this problem into two subproblems by setting (x + -0.4) equal to 0.217944947 and -0.217944947.Subproblem 1
x + -0.4 = 0.217944947 Simplifying x + -0.4 = 0.217944947 Reorder the terms: -0.4 + x = 0.217944947 Solving -0.4 + x = 0.217944947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.217944947 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.217944947 + 0.4 x = 0.217944947 + 0.4 Combine like terms: 0.217944947 + 0.4 = 0.617944947 x = 0.617944947 Simplifying x = 0.617944947Subproblem 2
x + -0.4 = -0.217944947 Simplifying x + -0.4 = -0.217944947 Reorder the terms: -0.4 + x = -0.217944947 Solving -0.4 + x = -0.217944947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.217944947 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.217944947 + 0.4 x = -0.217944947 + 0.4 Combine like terms: -0.217944947 + 0.4 = 0.182055053 x = 0.182055053 Simplifying x = 0.182055053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.617944947, 0.182055053}
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