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Simplifying 8x2 + 18x + -560 = 0 Reorder the terms: -560 + 18x + 8x2 = 0 Solving -560 + 18x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-280 + 9x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-280 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -280 + 9x + 4x2 = 0 Solving -280 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -70 + 2.25x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 2.25x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 2.25x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 2.25x + x2 = 0 + 70 2.25x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 2.25x + x2 = 70 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 70 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 70 + 1.265625 Combine like terms: 70 + 1.265625 = 71.265625 1.265625 + 2.25x + x2 = 71.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 71.265625 Calculate the square root of the right side: 8.441897002 Break this problem into two subproblems by setting (x + 1.125) equal to 8.441897002 and -8.441897002.Subproblem 1
x + 1.125 = 8.441897002 Simplifying x + 1.125 = 8.441897002 Reorder the terms: 1.125 + x = 8.441897002 Solving 1.125 + x = 8.441897002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 8.441897002 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 8.441897002 + -1.125 x = 8.441897002 + -1.125 Combine like terms: 8.441897002 + -1.125 = 7.316897002 x = 7.316897002 Simplifying x = 7.316897002Subproblem 2
x + 1.125 = -8.441897002 Simplifying x + 1.125 = -8.441897002 Reorder the terms: 1.125 + x = -8.441897002 Solving 1.125 + x = -8.441897002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -8.441897002 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -8.441897002 + -1.125 x = -8.441897002 + -1.125 Combine like terms: -8.441897002 + -1.125 = -9.566897002 x = -9.566897002 Simplifying x = -9.566897002Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.316897002, -9.566897002}Solution
x = {7.316897002, -9.566897002}
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