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Simplifying 85x2 + 10x = 180 Reorder the terms: 10x + 85x2 = 180 Solving 10x + 85x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 10x + 85x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 10x + 85x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 2x + 17x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + 2x + 17x2)' equal to zero and attempt to solve: Simplifying -36 + 2x + 17x2 = 0 Solving -36 + 2x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -2.117647059 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '2.117647059' to each side of the equation. -2.117647059 + 0.1176470588x + 2.117647059 + x2 = 0 + 2.117647059 Reorder the terms: -2.117647059 + 2.117647059 + 0.1176470588x + x2 = 0 + 2.117647059 Combine like terms: -2.117647059 + 2.117647059 = 0.000000000 0.000000000 + 0.1176470588x + x2 = 0 + 2.117647059 0.1176470588x + x2 = 0 + 2.117647059 Combine like terms: 0 + 2.117647059 = 2.117647059 0.1176470588x + x2 = 2.117647059 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 2.117647059 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 2.117647059 + 0.003460207611 Combine like terms: 2.117647059 + 0.003460207611 = 2.121107266611 0.003460207611 + 0.1176470588x + x2 = 2.121107266611 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 2.121107266611 Calculate the square root of the right side: 1.456402165 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 1.456402165 and -1.456402165.Subproblem 1
x + 0.0588235294 = 1.456402165 Simplifying x + 0.0588235294 = 1.456402165 Reorder the terms: 0.0588235294 + x = 1.456402165 Solving 0.0588235294 + x = 1.456402165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 1.456402165 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 1.456402165 + -0.0588235294 x = 1.456402165 + -0.0588235294 Combine like terms: 1.456402165 + -0.0588235294 = 1.3975786356 x = 1.3975786356 Simplifying x = 1.3975786356Subproblem 2
x + 0.0588235294 = -1.456402165 Simplifying x + 0.0588235294 = -1.456402165 Reorder the terms: 0.0588235294 + x = -1.456402165 Solving 0.0588235294 + x = -1.456402165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -1.456402165 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -1.456402165 + -0.0588235294 x = -1.456402165 + -0.0588235294 Combine like terms: -1.456402165 + -0.0588235294 = -1.5152256944 x = -1.5152256944 Simplifying x = -1.5152256944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3975786356, -1.5152256944}Solution
x = {1.3975786356, -1.5152256944}
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