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Simplifying 3.14x2 + -1x + -13(3.14) = 0 Multiply -13 * 3.14 3.14x2 + -1x + -40.82 = 0 Reorder the terms: -40.82 + -1x + 3.14x2 = 0 Solving -40.82 + -1x + 3.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -13 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -0.3184713376x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -0.3184713376x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -0.3184713376x + x2 = 0 + 13 -0.3184713376x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -0.3184713376x + x2 = 13 The x term is -0.3184713376x. Take half its coefficient (-0.1592356688). Square it (0.02535599822) and add it to both sides. Add '0.02535599822' to each side of the equation. -0.3184713376x + 0.02535599822 + x2 = 13 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 13 + 0.02535599822 Combine like terms: 13 + 0.02535599822 = 13.02535599822 0.02535599822 + -0.3184713376x + x2 = 13.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 13.02535599822 Calculate the square root of the right side: 3.609065807 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 3.609065807 and -3.609065807.Subproblem 1
x + -0.1592356688 = 3.609065807 Simplifying x + -0.1592356688 = 3.609065807 Reorder the terms: -0.1592356688 + x = 3.609065807 Solving -0.1592356688 + x = 3.609065807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = 3.609065807 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 3.609065807 + 0.1592356688 x = 3.609065807 + 0.1592356688 Combine like terms: 3.609065807 + 0.1592356688 = 3.7683014758 x = 3.7683014758 Simplifying x = 3.7683014758Subproblem 2
x + -0.1592356688 = -3.609065807 Simplifying x + -0.1592356688 = -3.609065807 Reorder the terms: -0.1592356688 + x = -3.609065807 Solving -0.1592356688 + x = -3.609065807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = -3.609065807 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -3.609065807 + 0.1592356688 x = -3.609065807 + 0.1592356688 Combine like terms: -3.609065807 + 0.1592356688 = -3.4498301382 x = -3.4498301382 Simplifying x = -3.4498301382Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7683014758, -3.4498301382}
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