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Simplifying -2.7x2 + 40x + 6.5 = 16 Reorder the terms: 6.5 + 40x + -2.7x2 = 16 Solving 6.5 + 40x + -2.7x2 = 16 Solving for variable 'x'. Reorder the terms: 6.5 + -16 + 40x + -2.7x2 = 16 + -16 Combine like terms: 6.5 + -16 = -9.5 -9.5 + 40x + -2.7x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -9.5 + 40x + -2.7x2 = 0 Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. 3.518518519 + -14.81481481x + x2 = 0 Move the constant term to the right: Add '-3.518518519' to each side of the equation. 3.518518519 + -14.81481481x + -3.518518519 + x2 = 0 + -3.518518519 Reorder the terms: 3.518518519 + -3.518518519 + -14.81481481x + x2 = 0 + -3.518518519 Combine like terms: 3.518518519 + -3.518518519 = 0.000000000 0.000000000 + -14.81481481x + x2 = 0 + -3.518518519 -14.81481481x + x2 = 0 + -3.518518519 Combine like terms: 0 + -3.518518519 = -3.518518519 -14.81481481x + x2 = -3.518518519 The x term is -14.81481481x. Take half its coefficient (-7.407407405). Square it (54.86968446) and add it to both sides. Add '54.86968446' to each side of the equation. -14.81481481x + 54.86968446 + x2 = -3.518518519 + 54.86968446 Reorder the terms: 54.86968446 + -14.81481481x + x2 = -3.518518519 + 54.86968446 Combine like terms: -3.518518519 + 54.86968446 = 51.351165941 54.86968446 + -14.81481481x + x2 = 51.351165941 Factor a perfect square on the left side: (x + -7.407407405)(x + -7.407407405) = 51.351165941 Calculate the square root of the right side: 7.165972784 Break this problem into two subproblems by setting (x + -7.407407405) equal to 7.165972784 and -7.165972784.Subproblem 1
x + -7.407407405 = 7.165972784 Simplifying x + -7.407407405 = 7.165972784 Reorder the terms: -7.407407405 + x = 7.165972784 Solving -7.407407405 + x = 7.165972784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.407407405' to each side of the equation. -7.407407405 + 7.407407405 + x = 7.165972784 + 7.407407405 Combine like terms: -7.407407405 + 7.407407405 = 0.000000000 0.000000000 + x = 7.165972784 + 7.407407405 x = 7.165972784 + 7.407407405 Combine like terms: 7.165972784 + 7.407407405 = 14.573380189 x = 14.573380189 Simplifying x = 14.573380189Subproblem 2
x + -7.407407405 = -7.165972784 Simplifying x + -7.407407405 = -7.165972784 Reorder the terms: -7.407407405 + x = -7.165972784 Solving -7.407407405 + x = -7.165972784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.407407405' to each side of the equation. -7.407407405 + 7.407407405 + x = -7.165972784 + 7.407407405 Combine like terms: -7.407407405 + 7.407407405 = 0.000000000 0.000000000 + x = -7.165972784 + 7.407407405 x = -7.165972784 + 7.407407405 Combine like terms: -7.165972784 + 7.407407405 = 0.241434621 x = 0.241434621 Simplifying x = 0.241434621Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.573380189, 0.241434621}
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