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Simplifying 4(x2 + -5x + 7) + -8(x2 + 4x + -5) = 0 Reorder the terms: 4(7 + -5x + x2) + -8(x2 + 4x + -5) = 0 (7 * 4 + -5x * 4 + x2 * 4) + -8(x2 + 4x + -5) = 0 (28 + -20x + 4x2) + -8(x2 + 4x + -5) = 0 Reorder the terms: 28 + -20x + 4x2 + -8(-5 + 4x + x2) = 0 28 + -20x + 4x2 + (-5 * -8 + 4x * -8 + x2 * -8) = 0 28 + -20x + 4x2 + (40 + -32x + -8x2) = 0 Reorder the terms: 28 + 40 + -20x + -32x + 4x2 + -8x2 = 0 Combine like terms: 28 + 40 = 68 68 + -20x + -32x + 4x2 + -8x2 = 0 Combine like terms: -20x + -32x = -52x 68 + -52x + 4x2 + -8x2 = 0 Combine like terms: 4x2 + -8x2 = -4x2 68 + -52x + -4x2 = 0 Solving 68 + -52x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(17 + -13x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(17 + -13x + -1x2)' equal to zero and attempt to solve: Simplifying 17 + -13x + -1x2 = 0 Solving 17 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + 13x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 13x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 13x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 13x + x2 = 0 + 17 13x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 13x + x2 = 17 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 17 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 17 + 42.25 Combine like terms: 17 + 42.25 = 59.25 42.25 + 13x + x2 = 59.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 6.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 6.5 = 7.697402159 Simplifying x + 6.5 = 7.697402159 Reorder the terms: 6.5 + x = 7.697402159 Solving 6.5 + x = 7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.697402159 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.697402159 + -6.5 x = 7.697402159 + -6.5 Combine like terms: 7.697402159 + -6.5 = 1.197402159 x = 1.197402159 Simplifying x = 1.197402159Subproblem 2
x + 6.5 = -7.697402159 Simplifying x + 6.5 = -7.697402159 Reorder the terms: 6.5 + x = -7.697402159 Solving 6.5 + x = -7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.697402159 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.697402159 + -6.5 x = -7.697402159 + -6.5 Combine like terms: -7.697402159 + -6.5 = -14.197402159 x = -14.197402159 Simplifying x = -14.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.197402159, -14.197402159}Solution
x = {1.197402159, -14.197402159}
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