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Simplifying -4x2 + 56x + -144 = 0 Reorder the terms: -144 + 56x + -4x2 = 0 Solving -144 + 56x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + 14x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-36 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying -36 + 14x + -1x2 = 0 Solving -36 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -14x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -14x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -14x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -14x + x2 = 0 + -36 -14x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -14x + x2 = -36 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -36 + 49 Reorder the terms: 49 + -14x + x2 = -36 + 49 Combine like terms: -36 + 49 = 13 49 + -14x + x2 = 13 Factor a perfect square on the left side: (x + -7)(x + -7) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -7) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -7 = 3.605551275 Simplifying x + -7 = 3.605551275 Reorder the terms: -7 + x = 3.605551275 Solving -7 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.605551275 + 7 x = 3.605551275 + 7 Combine like terms: 3.605551275 + 7 = 10.605551275 x = 10.605551275 Simplifying x = 10.605551275Subproblem 2
x + -7 = -3.605551275 Simplifying x + -7 = -3.605551275 Reorder the terms: -7 + x = -3.605551275 Solving -7 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.605551275 + 7 x = -3.605551275 + 7 Combine like terms: -3.605551275 + 7 = 3.394448725 x = 3.394448725 Simplifying x = 3.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.605551275, 3.394448725}Solution
x = {10.605551275, 3.394448725}
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