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Simplifying 8[7 + -1x(-4x + -7)] = 128 + 280 Reorder the terms: 8[7 + -1x(-7 + -4x)] = 128 + 280 8[7 + (-7 * -1x + -4x * -1x)] = 128 + 280 8[7 + (7x + 4x2)] = 128 + 280 [7 * 8 + 7x * 8 + 4x2 * 8] = 128 + 280 [56 + 56x + 32x2] = 128 + 280 Combine like terms: 128 + 280 = 408 56 + 56x + 32x2 = 408 Solving 56 + 56x + 32x2 = 408 Solving for variable 'x'. Reorder the terms: 56 + -408 + 56x + 32x2 = 408 + -408 Combine like terms: 56 + -408 = -352 -352 + 56x + 32x2 = 408 + -408 Combine like terms: 408 + -408 = 0 -352 + 56x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-44 + 7x + 4x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-44 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -44 + 7x + 4x2 = 0 Solving -44 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11 + 1.75x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 1.75x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 1.75x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 1.75x + x2 = 0 + 11 1.75x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 1.75x + x2 = 11 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 11 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 11 + 0.765625 Combine like terms: 11 + 0.765625 = 11.765625 0.765625 + 1.75x + x2 = 11.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 11.765625 Calculate the square root of the right side: 3.430105684 Break this problem into two subproblems by setting (x + 0.875) equal to 3.430105684 and -3.430105684.Subproblem 1
x + 0.875 = 3.430105684 Simplifying x + 0.875 = 3.430105684 Reorder the terms: 0.875 + x = 3.430105684 Solving 0.875 + x = 3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 3.430105684 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 3.430105684 + -0.875 x = 3.430105684 + -0.875 Combine like terms: 3.430105684 + -0.875 = 2.555105684 x = 2.555105684 Simplifying x = 2.555105684Subproblem 2
x + 0.875 = -3.430105684 Simplifying x + 0.875 = -3.430105684 Reorder the terms: 0.875 + x = -3.430105684 Solving 0.875 + x = -3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -3.430105684 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -3.430105684 + -0.875 x = -3.430105684 + -0.875 Combine like terms: -3.430105684 + -0.875 = -4.305105684 x = -4.305105684 Simplifying x = -4.305105684Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.555105684, -4.305105684}Solution
x = {2.555105684, -4.305105684}
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