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Simplifying 170 = 36x + 8x2 Solving 170 = 36x + 8x2 Solving for variable 'x'. Reorder the terms: 170 + -36x + -8x2 = 36x + -36x + 8x2 + -8x2 Combine like terms: 36x + -36x = 0 170 + -36x + -8x2 = 0 + 8x2 + -8x2 170 + -36x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 170 + -36x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(85 + -18x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(85 + -18x + -4x2)' equal to zero and attempt to solve: Simplifying 85 + -18x + -4x2 = 0 Solving 85 + -18x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -21.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '21.25' to each side of the equation. -21.25 + 4.5x + 21.25 + x2 = 0 + 21.25 Reorder the terms: -21.25 + 21.25 + 4.5x + x2 = 0 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + 4.5x + x2 = 0 + 21.25 4.5x + x2 = 0 + 21.25 Combine like terms: 0 + 21.25 = 21.25 4.5x + x2 = 21.25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 21.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 21.25 + 5.0625 Combine like terms: 21.25 + 5.0625 = 26.3125 5.0625 + 4.5x + x2 = 26.3125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 26.3125 Calculate the square root of the right side: 5.129571132 Break this problem into two subproblems by setting (x + 2.25) equal to 5.129571132 and -5.129571132.Subproblem 1
x + 2.25 = 5.129571132 Simplifying x + 2.25 = 5.129571132 Reorder the terms: 2.25 + x = 5.129571132 Solving 2.25 + x = 5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.129571132 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.129571132 + -2.25 x = 5.129571132 + -2.25 Combine like terms: 5.129571132 + -2.25 = 2.879571132 x = 2.879571132 Simplifying x = 2.879571132Subproblem 2
x + 2.25 = -5.129571132 Simplifying x + 2.25 = -5.129571132 Reorder the terms: 2.25 + x = -5.129571132 Solving 2.25 + x = -5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.129571132 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.129571132 + -2.25 x = -5.129571132 + -2.25 Combine like terms: -5.129571132 + -2.25 = -7.379571132 x = -7.379571132 Simplifying x = -7.379571132Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.879571132, -7.379571132}Solution
x = {2.879571132, -7.379571132}
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