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Simplifying 0 = -0.0742x2 + 1.3982x + 50.396 Reorder the terms: 0 = 50.396 + 1.3982x + -0.0742x2 Solving 0 = 50.396 + 1.3982x + -0.0742x2 Solving for variable 'x'. Combine like terms: 0 + -50.396 = -50.396 -50.396 + -1.3982x + 0.0742x2 = 50.396 + 1.3982x + -0.0742x2 + -50.396 + -1.3982x + 0.0742x2 Reorder the terms: -50.396 + -1.3982x + 0.0742x2 = 50.396 + -50.396 + 1.3982x + -1.3982x + -0.0742x2 + 0.0742x2 Combine like terms: 50.396 + -50.396 = 0.000 -50.396 + -1.3982x + 0.0742x2 = 0.000 + 1.3982x + -1.3982x + -0.0742x2 + 0.0742x2 -50.396 + -1.3982x + 0.0742x2 = 1.3982x + -1.3982x + -0.0742x2 + 0.0742x2 Combine like terms: 1.3982x + -1.3982x = 0.0000 -50.396 + -1.3982x + 0.0742x2 = 0.0000 + -0.0742x2 + 0.0742x2 -50.396 + -1.3982x + 0.0742x2 = -0.0742x2 + 0.0742x2 Combine like terms: -0.0742x2 + 0.0742x2 = 0.0000 -50.396 + -1.3982x + 0.0742x2 = 0.0000 Begin completing the square. Divide all terms by 0.0742 the coefficient of the squared term: Divide each side by '0.0742'. -679.1913747 + -18.84366577x + x2 = 0 Move the constant term to the right: Add '679.1913747' to each side of the equation. -679.1913747 + -18.84366577x + 679.1913747 + x2 = 0 + 679.1913747 Reorder the terms: -679.1913747 + 679.1913747 + -18.84366577x + x2 = 0 + 679.1913747 Combine like terms: -679.1913747 + 679.1913747 = 0.0000000 0.0000000 + -18.84366577x + x2 = 0 + 679.1913747 -18.84366577x + x2 = 0 + 679.1913747 Combine like terms: 0 + 679.1913747 = 679.1913747 -18.84366577x + x2 = 679.1913747 The x term is -18.84366577x. Take half its coefficient (-9.421832885). Square it (88.77093491) and add it to both sides. Add '88.77093491' to each side of the equation. -18.84366577x + 88.77093491 + x2 = 679.1913747 + 88.77093491 Reorder the terms: 88.77093491 + -18.84366577x + x2 = 679.1913747 + 88.77093491 Combine like terms: 679.1913747 + 88.77093491 = 767.96230961 88.77093491 + -18.84366577x + x2 = 767.96230961 Factor a perfect square on the left side: (x + -9.421832885)(x + -9.421832885) = 767.96230961 Calculate the square root of the right side: 27.712132895 Break this problem into two subproblems by setting (x + -9.421832885) equal to 27.712132895 and -27.712132895.Subproblem 1
x + -9.421832885 = 27.712132895 Simplifying x + -9.421832885 = 27.712132895 Reorder the terms: -9.421832885 + x = 27.712132895 Solving -9.421832885 + x = 27.712132895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.421832885' to each side of the equation. -9.421832885 + 9.421832885 + x = 27.712132895 + 9.421832885 Combine like terms: -9.421832885 + 9.421832885 = 0.000000000 0.000000000 + x = 27.712132895 + 9.421832885 x = 27.712132895 + 9.421832885 Combine like terms: 27.712132895 + 9.421832885 = 37.13396578 x = 37.13396578 Simplifying x = 37.13396578Subproblem 2
x + -9.421832885 = -27.712132895 Simplifying x + -9.421832885 = -27.712132895 Reorder the terms: -9.421832885 + x = -27.712132895 Solving -9.421832885 + x = -27.712132895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.421832885' to each side of the equation. -9.421832885 + 9.421832885 + x = -27.712132895 + 9.421832885 Combine like terms: -9.421832885 + 9.421832885 = 0.000000000 0.000000000 + x = -27.712132895 + 9.421832885 x = -27.712132895 + 9.421832885 Combine like terms: -27.712132895 + 9.421832885 = -18.29030001 x = -18.29030001 Simplifying x = -18.29030001Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.13396578, -18.29030001}
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