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Simplifying 65x2 + -79x + 24 = 646 Reorder the terms: 24 + -79x + 65x2 = 646 Solving 24 + -79x + 65x2 = 646 Solving for variable 'x'. Reorder the terms: 24 + -646 + -79x + 65x2 = 646 + -646 Combine like terms: 24 + -646 = -622 -622 + -79x + 65x2 = 646 + -646 Combine like terms: 646 + -646 = 0 -622 + -79x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. -9.569230769 + -1.215384615x + x2 = 0 Move the constant term to the right: Add '9.569230769' to each side of the equation. -9.569230769 + -1.215384615x + 9.569230769 + x2 = 0 + 9.569230769 Reorder the terms: -9.569230769 + 9.569230769 + -1.215384615x + x2 = 0 + 9.569230769 Combine like terms: -9.569230769 + 9.569230769 = 0.000000000 0.000000000 + -1.215384615x + x2 = 0 + 9.569230769 -1.215384615x + x2 = 0 + 9.569230769 Combine like terms: 0 + 9.569230769 = 9.569230769 -1.215384615x + x2 = 9.569230769 The x term is -1.215384615x. Take half its coefficient (-0.6076923075). Square it (0.3692899406) and add it to both sides. Add '0.3692899406' to each side of the equation. -1.215384615x + 0.3692899406 + x2 = 9.569230769 + 0.3692899406 Reorder the terms: 0.3692899406 + -1.215384615x + x2 = 9.569230769 + 0.3692899406 Combine like terms: 9.569230769 + 0.3692899406 = 9.9385207096 0.3692899406 + -1.215384615x + x2 = 9.9385207096 Factor a perfect square on the left side: (x + -0.6076923075)(x + -0.6076923075) = 9.9385207096 Calculate the square root of the right side: 3.152541944 Break this problem into two subproblems by setting (x + -0.6076923075) equal to 3.152541944 and -3.152541944.Subproblem 1
x + -0.6076923075 = 3.152541944 Simplifying x + -0.6076923075 = 3.152541944 Reorder the terms: -0.6076923075 + x = 3.152541944 Solving -0.6076923075 + x = 3.152541944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6076923075' to each side of the equation. -0.6076923075 + 0.6076923075 + x = 3.152541944 + 0.6076923075 Combine like terms: -0.6076923075 + 0.6076923075 = 0.0000000000 0.0000000000 + x = 3.152541944 + 0.6076923075 x = 3.152541944 + 0.6076923075 Combine like terms: 3.152541944 + 0.6076923075 = 3.7602342515 x = 3.7602342515 Simplifying x = 3.7602342515Subproblem 2
x + -0.6076923075 = -3.152541944 Simplifying x + -0.6076923075 = -3.152541944 Reorder the terms: -0.6076923075 + x = -3.152541944 Solving -0.6076923075 + x = -3.152541944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6076923075' to each side of the equation. -0.6076923075 + 0.6076923075 + x = -3.152541944 + 0.6076923075 Combine like terms: -0.6076923075 + 0.6076923075 = 0.0000000000 0.0000000000 + x = -3.152541944 + 0.6076923075 x = -3.152541944 + 0.6076923075 Combine like terms: -3.152541944 + 0.6076923075 = -2.5448496365 x = -2.5448496365 Simplifying x = -2.5448496365Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7602342515, -2.5448496365}
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