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Simplifying 80 = 5x + 5.65x2 Solving 80 = 5x + 5.65x2 Solving for variable 'x'. Reorder the terms: 80 + -5x + -5.65x2 = 5x + -5x + 5.65x2 + -5.65x2 Combine like terms: 5x + -5x = 0 80 + -5x + -5.65x2 = 0 + 5.65x2 + -5.65x2 80 + -5x + -5.65x2 = 5.65x2 + -5.65x2 Combine like terms: 5.65x2 + -5.65x2 = 0.00 80 + -5x + -5.65x2 = 0.00 Begin completing the square. Divide all terms by -5.65 the coefficient of the squared term: Divide each side by '-5.65'. -14.15929204 + 0.8849557522x + x2 = 0 Move the constant term to the right: Add '14.15929204' to each side of the equation. -14.15929204 + 0.8849557522x + 14.15929204 + x2 = 0 + 14.15929204 Reorder the terms: -14.15929204 + 14.15929204 + 0.8849557522x + x2 = 0 + 14.15929204 Combine like terms: -14.15929204 + 14.15929204 = 0.00000000 0.00000000 + 0.8849557522x + x2 = 0 + 14.15929204 0.8849557522x + x2 = 0 + 14.15929204 Combine like terms: 0 + 14.15929204 = 14.15929204 0.8849557522x + x2 = 14.15929204 The x term is 0.8849557522x. Take half its coefficient (0.4424778761). Square it (0.1957866708) and add it to both sides. Add '0.1957866708' to each side of the equation. 0.8849557522x + 0.1957866708 + x2 = 14.15929204 + 0.1957866708 Reorder the terms: 0.1957866708 + 0.8849557522x + x2 = 14.15929204 + 0.1957866708 Combine like terms: 14.15929204 + 0.1957866708 = 14.3550787108 0.1957866708 + 0.8849557522x + x2 = 14.3550787108 Factor a perfect square on the left side: (x + 0.4424778761)(x + 0.4424778761) = 14.3550787108 Calculate the square root of the right side: 3.788809669 Break this problem into two subproblems by setting (x + 0.4424778761) equal to 3.788809669 and -3.788809669.Subproblem 1
x + 0.4424778761 = 3.788809669 Simplifying x + 0.4424778761 = 3.788809669 Reorder the terms: 0.4424778761 + x = 3.788809669 Solving 0.4424778761 + x = 3.788809669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4424778761' to each side of the equation. 0.4424778761 + -0.4424778761 + x = 3.788809669 + -0.4424778761 Combine like terms: 0.4424778761 + -0.4424778761 = 0.0000000000 0.0000000000 + x = 3.788809669 + -0.4424778761 x = 3.788809669 + -0.4424778761 Combine like terms: 3.788809669 + -0.4424778761 = 3.3463317929 x = 3.3463317929 Simplifying x = 3.3463317929Subproblem 2
x + 0.4424778761 = -3.788809669 Simplifying x + 0.4424778761 = -3.788809669 Reorder the terms: 0.4424778761 + x = -3.788809669 Solving 0.4424778761 + x = -3.788809669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4424778761' to each side of the equation. 0.4424778761 + -0.4424778761 + x = -3.788809669 + -0.4424778761 Combine like terms: 0.4424778761 + -0.4424778761 = 0.0000000000 0.0000000000 + x = -3.788809669 + -0.4424778761 x = -3.788809669 + -0.4424778761 Combine like terms: -3.788809669 + -0.4424778761 = -4.2312875451 x = -4.2312875451 Simplifying x = -4.2312875451Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3463317929, -4.2312875451}
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