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Simplifying (2x + -5)(x + -7) = 4x(x + -1) Reorder the terms: (-5 + 2x)(x + -7) = 4x(x + -1) Reorder the terms: (-5 + 2x)(-7 + x) = 4x(x + -1) Multiply (-5 + 2x) * (-7 + x) (-5(-7 + x) + 2x * (-7 + x)) = 4x(x + -1) ((-7 * -5 + x * -5) + 2x * (-7 + x)) = 4x(x + -1) ((35 + -5x) + 2x * (-7 + x)) = 4x(x + -1) (35 + -5x + (-7 * 2x + x * 2x)) = 4x(x + -1) (35 + -5x + (-14x + 2x2)) = 4x(x + -1) Combine like terms: -5x + -14x = -19x (35 + -19x + 2x2) = 4x(x + -1) Reorder the terms: 35 + -19x + 2x2 = 4x(-1 + x) 35 + -19x + 2x2 = (-1 * 4x + x * 4x) 35 + -19x + 2x2 = (-4x + 4x2) Solving 35 + -19x + 2x2 = -4x + 4x2 Solving for variable 'x'. Reorder the terms: 35 + -19x + 4x + 2x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: -19x + 4x = -15x 35 + -15x + 2x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 35 + -15x + -2x2 = -4x + 4x2 + 4x + -4x2 Reorder the terms: 35 + -15x + -2x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 35 + -15x + -2x2 = 0 + 4x2 + -4x2 35 + -15x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 35 + -15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -17.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 7.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 7.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 7.5x + x2 = 0 + 17.5 7.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 7.5x + x2 = 17.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 17.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 17.5 + 14.0625 Combine like terms: 17.5 + 14.0625 = 31.5625 14.0625 + 7.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + 3.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + 3.75 = 5.618051264 Simplifying x + 3.75 = 5.618051264 Reorder the terms: 3.75 + x = 5.618051264 Solving 3.75 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 5.618051264 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.618051264 + -3.75 x = 5.618051264 + -3.75 Combine like terms: 5.618051264 + -3.75 = 1.868051264 x = 1.868051264 Simplifying x = 1.868051264Subproblem 2
x + 3.75 = -5.618051264 Simplifying x + 3.75 = -5.618051264 Reorder the terms: 3.75 + x = -5.618051264 Solving 3.75 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -5.618051264 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.618051264 + -3.75 x = -5.618051264 + -3.75 Combine like terms: -5.618051264 + -3.75 = -9.368051264 x = -9.368051264 Simplifying x = -9.368051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.868051264, -9.368051264}
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