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Simplifying 0.001415168x2 + -0.246295547x + 0.0000256561 = 0 Reorder the terms: 0.0000256561 + -0.246295547x + 0.001415168x2 = 0 Solving 0.0000256561 + -0.246295547x + 0.001415168x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.001415168 the coefficient of the squared term: Divide each side by '0.001415168'. 0.01812936697 + -174.0397939x + x2 = 0 Move the constant term to the right: Add '-0.01812936697' to each side of the equation. 0.01812936697 + -174.0397939x + -0.01812936697 + x2 = 0 + -0.01812936697 Reorder the terms: 0.01812936697 + -0.01812936697 + -174.0397939x + x2 = 0 + -0.01812936697 Combine like terms: 0.01812936697 + -0.01812936697 = 0.00000000000 0.00000000000 + -174.0397939x + x2 = 0 + -0.01812936697 -174.0397939x + x2 = 0 + -0.01812936697 Combine like terms: 0 + -0.01812936697 = -0.01812936697 -174.0397939x + x2 = -0.01812936697 The x term is -174.0397939x. Take half its coefficient (-87.01989695). Square it (7572.462465) and add it to both sides. Add '7572.462465' to each side of the equation. -174.0397939x + 7572.462465 + x2 = -0.01812936697 + 7572.462465 Reorder the terms: 7572.462465 + -174.0397939x + x2 = -0.01812936697 + 7572.462465 Combine like terms: -0.01812936697 + 7572.462465 = 7572.44433563303 7572.462465 + -174.0397939x + x2 = 7572.44433563303 Factor a perfect square on the left side: (x + -87.01989695)(x + -87.01989695) = 7572.44433563303 Calculate the square root of the right side: 87.019792781 Break this problem into two subproblems by setting (x + -87.01989695) equal to 87.019792781 and -87.019792781.Subproblem 1
x + -87.01989695 = 87.019792781 Simplifying x + -87.01989695 = 87.019792781 Reorder the terms: -87.01989695 + x = 87.019792781 Solving -87.01989695 + x = 87.019792781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.01989695' to each side of the equation. -87.01989695 + 87.01989695 + x = 87.019792781 + 87.01989695 Combine like terms: -87.01989695 + 87.01989695 = 0.00000000 0.00000000 + x = 87.019792781 + 87.01989695 x = 87.019792781 + 87.01989695 Combine like terms: 87.019792781 + 87.01989695 = 174.039689731 x = 174.039689731 Simplifying x = 174.039689731Subproblem 2
x + -87.01989695 = -87.019792781 Simplifying x + -87.01989695 = -87.019792781 Reorder the terms: -87.01989695 + x = -87.019792781 Solving -87.01989695 + x = -87.019792781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.01989695' to each side of the equation. -87.01989695 + 87.01989695 + x = -87.019792781 + 87.01989695 Combine like terms: -87.01989695 + 87.01989695 = 0.00000000 0.00000000 + x = -87.019792781 + 87.01989695 x = -87.019792781 + 87.01989695 Combine like terms: -87.019792781 + 87.01989695 = 0.000104169 x = 0.000104169 Simplifying x = 0.000104169Solution
The solution to the problem is based on the solutions from the subproblems. x = {174.039689731, 0.000104169}
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