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Simplifying 3.14x2 + -1x + -20(3.14) = 0 Multiply -20 * 3.14 3.14x2 + -1x + -62.8 = 0 Reorder the terms: -62.8 + -1x + 3.14x2 = 0 Solving -62.8 + -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'. -20 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.3184713376x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -0.3184713376x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.3184713376x + x2 = 0 + 20 -0.3184713376x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.3184713376x + x2 = 20 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 = 20 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 20 + 0.02535599822 Combine like terms: 20 + 0.02535599822 = 20.02535599822 0.02535599822 + -0.3184713376x + x2 = 20.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 20.02535599822 Calculate the square root of the right side: 4.474969944 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 4.474969944 and -4.474969944.Subproblem 1
x + -0.1592356688 = 4.474969944 Simplifying x + -0.1592356688 = 4.474969944 Reorder the terms: -0.1592356688 + x = 4.474969944 Solving -0.1592356688 + x = 4.474969944 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 = 4.474969944 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 4.474969944 + 0.1592356688 x = 4.474969944 + 0.1592356688 Combine like terms: 4.474969944 + 0.1592356688 = 4.6342056128 x = 4.6342056128 Simplifying x = 4.6342056128Subproblem 2
x + -0.1592356688 = -4.474969944 Simplifying x + -0.1592356688 = -4.474969944 Reorder the terms: -0.1592356688 + x = -4.474969944 Solving -0.1592356688 + x = -4.474969944 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 = -4.474969944 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -4.474969944 + 0.1592356688 x = -4.474969944 + 0.1592356688 Combine like terms: -4.474969944 + 0.1592356688 = -4.3157342752 x = -4.3157342752 Simplifying x = -4.3157342752Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6342056128, -4.3157342752}
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