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Simplifying 1.71 + -90 * 9.41x + -1.29 * 900x2 = 0 Multiply -90 * 9.41 1.71 + -846.9x + -1.29 * 900x2 = 0 Multiply -1.29 * 900 1.71 + -846.9x + -1161x2 = 0 Solving 1.71 + -846.9x + -1161x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1161 the coefficient of the squared term: Divide each side by '-1161'. -0.001472868217 + 0.7294573643x + x2 = 0 Move the constant term to the right: Add '0.001472868217' to each side of the equation. -0.001472868217 + 0.7294573643x + 0.001472868217 + x2 = 0 + 0.001472868217 Reorder the terms: -0.001472868217 + 0.001472868217 + 0.7294573643x + x2 = 0 + 0.001472868217 Combine like terms: -0.001472868217 + 0.001472868217 = 0.000000000000 0.000000000000 + 0.7294573643x + x2 = 0 + 0.001472868217 0.7294573643x + x2 = 0 + 0.001472868217 Combine like terms: 0 + 0.001472868217 = 0.001472868217 0.7294573643x + x2 = 0.001472868217 The x term is 0.7294573643x. Take half its coefficient (0.3647286822). Square it (0.1330270116) and add it to both sides. Add '0.1330270116' to each side of the equation. 0.7294573643x + 0.1330270116 + x2 = 0.001472868217 + 0.1330270116 Reorder the terms: 0.1330270116 + 0.7294573643x + x2 = 0.001472868217 + 0.1330270116 Combine like terms: 0.001472868217 + 0.1330270116 = 0.134499879817 0.1330270116 + 0.7294573643x + x2 = 0.134499879817 Factor a perfect square on the left side: (x + 0.3647286822)(x + 0.3647286822) = 0.134499879817 Calculate the square root of the right side: 0.366742253 Break this problem into two subproblems by setting (x + 0.3647286822) equal to 0.366742253 and -0.366742253.Subproblem 1
x + 0.3647286822 = 0.366742253 Simplifying x + 0.3647286822 = 0.366742253 Reorder the terms: 0.3647286822 + x = 0.366742253 Solving 0.3647286822 + x = 0.366742253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3647286822' to each side of the equation. 0.3647286822 + -0.3647286822 + x = 0.366742253 + -0.3647286822 Combine like terms: 0.3647286822 + -0.3647286822 = 0.0000000000 0.0000000000 + x = 0.366742253 + -0.3647286822 x = 0.366742253 + -0.3647286822 Combine like terms: 0.366742253 + -0.3647286822 = 0.0020135708 x = 0.0020135708 Simplifying x = 0.0020135708Subproblem 2
x + 0.3647286822 = -0.366742253 Simplifying x + 0.3647286822 = -0.366742253 Reorder the terms: 0.3647286822 + x = -0.366742253 Solving 0.3647286822 + x = -0.366742253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3647286822' to each side of the equation. 0.3647286822 + -0.3647286822 + x = -0.366742253 + -0.3647286822 Combine like terms: 0.3647286822 + -0.3647286822 = 0.0000000000 0.0000000000 + x = -0.366742253 + -0.3647286822 x = -0.366742253 + -0.3647286822 Combine like terms: -0.366742253 + -0.3647286822 = -0.7314709352 x = -0.7314709352 Simplifying x = -0.7314709352Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0020135708, -0.7314709352}
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