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Simplifying -4x(2x + -3) = -5x + 5 Reorder the terms: -4x(-3 + 2x) = -5x + 5 (-3 * -4x + 2x * -4x) = -5x + 5 (12x + -8x2) = -5x + 5 Reorder the terms: 12x + -8x2 = 5 + -5x Solving 12x + -8x2 = 5 + -5x Solving for variable 'x'. Reorder the terms: -5 + 12x + 5x + -8x2 = 5 + -5x + -5 + 5x Combine like terms: 12x + 5x = 17x -5 + 17x + -8x2 = 5 + -5x + -5 + 5x Reorder the terms: -5 + 17x + -8x2 = 5 + -5 + -5x + 5x Combine like terms: 5 + -5 = 0 -5 + 17x + -8x2 = 0 + -5x + 5x -5 + 17x + -8x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -5 + 17x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.625 + -2.125x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2.125x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2.125x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2.125x + x2 = 0 + -0.625 -2.125x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2.125x + x2 = -0.625 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = -0.625 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = -0.625 + 1.12890625 Combine like terms: -0.625 + 1.12890625 = 0.50390625 1.12890625 + -2.125x + x2 = 0.50390625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (x + -1.0625) equal to 0.709863543 and -0.709863543.Subproblem 1
x + -1.0625 = 0.709863543 Simplifying x + -1.0625 = 0.709863543 Reorder the terms: -1.0625 + x = 0.709863543 Solving -1.0625 + x = 0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 0.709863543 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 0.709863543 + 1.0625 x = 0.709863543 + 1.0625 Combine like terms: 0.709863543 + 1.0625 = 1.772363543 x = 1.772363543 Simplifying x = 1.772363543Subproblem 2
x + -1.0625 = -0.709863543 Simplifying x + -1.0625 = -0.709863543 Reorder the terms: -1.0625 + x = -0.709863543 Solving -1.0625 + x = -0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -0.709863543 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -0.709863543 + 1.0625 x = -0.709863543 + 1.0625 Combine like terms: -0.709863543 + 1.0625 = 0.352636457 x = 0.352636457 Simplifying x = 0.352636457Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.772363543, 0.352636457}
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