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Simplifying 5[x(4x + -5)] = 3 + -2x Reorder the terms: 5[x(-5 + 4x)] = 3 + -2x 5[(-5 * x + 4x * x)] = 3 + -2x 5[(-5x + 4x2)] = 3 + -2x [-5x * 5 + 4x2 * 5] = 3 + -2x [-25x + 20x2] = 3 + -2x Solving -25x + 20x2 = 3 + -2x Solving for variable 'x'. Reorder the terms: -3 + -25x + 2x + 20x2 = 3 + -2x + -3 + 2x Combine like terms: -25x + 2x = -23x -3 + -23x + 20x2 = 3 + -2x + -3 + 2x Reorder the terms: -3 + -23x + 20x2 = 3 + -3 + -2x + 2x Combine like terms: 3 + -3 = 0 -3 + -23x + 20x2 = 0 + -2x + 2x -3 + -23x + 20x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -3 + -23x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.15 + -1.15x + x2 = 0.0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + -1.15x + 0.15 + x2 = 0.0 + 0.15 Reorder the terms: -0.15 + 0.15 + -1.15x + x2 = 0.0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + -1.15x + x2 = 0.0 + 0.15 -1.15x + x2 = 0.0 + 0.15 Combine like terms: 0.0 + 0.15 = 0.15 -1.15x + x2 = 0.15 The x term is -1.15x. Take half its coefficient (-0.575). Square it (0.330625) and add it to both sides. Add '0.330625' to each side of the equation. -1.15x + 0.330625 + x2 = 0.15 + 0.330625 Reorder the terms: 0.330625 + -1.15x + x2 = 0.15 + 0.330625 Combine like terms: 0.15 + 0.330625 = 0.480625 0.330625 + -1.15x + x2 = 0.480625 Factor a perfect square on the left side: (x + -0.575)(x + -0.575) = 0.480625 Calculate the square root of the right side: 0.693271231 Break this problem into two subproblems by setting (x + -0.575) equal to 0.693271231 and -0.693271231.Subproblem 1
x + -0.575 = 0.693271231 Simplifying x + -0.575 = 0.693271231 Reorder the terms: -0.575 + x = 0.693271231 Solving -0.575 + x = 0.693271231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.575' to each side of the equation. -0.575 + 0.575 + x = 0.693271231 + 0.575 Combine like terms: -0.575 + 0.575 = 0.000 0.000 + x = 0.693271231 + 0.575 x = 0.693271231 + 0.575 Combine like terms: 0.693271231 + 0.575 = 1.268271231 x = 1.268271231 Simplifying x = 1.268271231Subproblem 2
x + -0.575 = -0.693271231 Simplifying x + -0.575 = -0.693271231 Reorder the terms: -0.575 + x = -0.693271231 Solving -0.575 + x = -0.693271231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.575' to each side of the equation. -0.575 + 0.575 + x = -0.693271231 + 0.575 Combine like terms: -0.575 + 0.575 = 0.000 0.000 + x = -0.693271231 + 0.575 x = -0.693271231 + 0.575 Combine like terms: -0.693271231 + 0.575 = -0.118271231 x = -0.118271231 Simplifying x = -0.118271231Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.268271231, -0.118271231}
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