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Simplifying x = 2(5x + -1)(3x + 1) Reorder the terms: x = 2(-1 + 5x)(3x + 1) Reorder the terms: x = 2(-1 + 5x)(1 + 3x) Multiply (-1 + 5x) * (1 + 3x) x = 2(-1(1 + 3x) + 5x * (1 + 3x)) x = 2((1 * -1 + 3x * -1) + 5x * (1 + 3x)) x = 2((-1 + -3x) + 5x * (1 + 3x)) x = 2(-1 + -3x + (1 * 5x + 3x * 5x)) x = 2(-1 + -3x + (5x + 15x2)) Combine like terms: -3x + 5x = 2x x = 2(-1 + 2x + 15x2) x = (-1 * 2 + 2x * 2 + 15x2 * 2) x = (-2 + 4x + 30x2) Solving x = -2 + 4x + 30x2 Solving for variable 'x'. Reorder the terms: 2 + x + -4x + -30x2 = -2 + 4x + 30x2 + 2 + -4x + -30x2 Combine like terms: x + -4x = -3x 2 + -3x + -30x2 = -2 + 4x + 30x2 + 2 + -4x + -30x2 Reorder the terms: 2 + -3x + -30x2 = -2 + 2 + 4x + -4x + 30x2 + -30x2 Combine like terms: -2 + 2 = 0 2 + -3x + -30x2 = 0 + 4x + -4x + 30x2 + -30x2 2 + -3x + -30x2 = 4x + -4x + 30x2 + -30x2 Combine like terms: 4x + -4x = 0 2 + -3x + -30x2 = 0 + 30x2 + -30x2 2 + -3x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 2 + -3x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. -0.06666666667 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + 0.1x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + 0.1x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + 0.1x + x2 = 0 + 0.06666666667 0.1x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 0.1x + x2 = 0.06666666667 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.06666666667 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.06666666667 + 0.0025 Combine like terms: 0.06666666667 + 0.0025 = 0.06916666667 0.0025 + 0.1x + x2 = 0.06916666667 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.06916666667 Calculate the square root of the right side: 0.262995564 Break this problem into two subproblems by setting (x + 0.05) equal to 0.262995564 and -0.262995564.Subproblem 1
x + 0.05 = 0.262995564 Simplifying x + 0.05 = 0.262995564 Reorder the terms: 0.05 + x = 0.262995564 Solving 0.05 + x = 0.262995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.262995564 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.262995564 + -0.05 x = 0.262995564 + -0.05 Combine like terms: 0.262995564 + -0.05 = 0.212995564 x = 0.212995564 Simplifying x = 0.212995564Subproblem 2
x + 0.05 = -0.262995564 Simplifying x + 0.05 = -0.262995564 Reorder the terms: 0.05 + x = -0.262995564 Solving 0.05 + x = -0.262995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.262995564 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.262995564 + -0.05 x = -0.262995564 + -0.05 Combine like terms: -0.262995564 + -0.05 = -0.312995564 x = -0.312995564 Simplifying x = -0.312995564Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.212995564, -0.312995564}
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