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Simplifying 90 = 1.2x2 + 10x Reorder the terms: 90 = 10x + 1.2x2 Solving 90 = 10x + 1.2x2 Solving for variable 'x'. Reorder the terms: 90 + -10x + -1.2x2 = 10x + -10x + 1.2x2 + -1.2x2 Combine like terms: 10x + -10x = 0 90 + -10x + -1.2x2 = 0 + 1.2x2 + -1.2x2 90 + -10x + -1.2x2 = 1.2x2 + -1.2x2 Combine like terms: 1.2x2 + -1.2x2 = 0.0 90 + -10x + -1.2x2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -75 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 8.333333333x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 8.333333333x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 8.333333333x + x2 = 0 + 75 8.333333333x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 8.333333333x + x2 = 75 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = 75 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = 75 + 17.36111111 Combine like terms: 75 + 17.36111111 = 92.36111111 17.36111111 + 8.333333333x + x2 = 92.36111111 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 92.36111111 Calculate the square root of the right side: 9.610468829 Break this problem into two subproblems by setting (x + 4.166666667) equal to 9.610468829 and -9.610468829.Subproblem 1
x + 4.166666667 = 9.610468829 Simplifying x + 4.166666667 = 9.610468829 Reorder the terms: 4.166666667 + x = 9.610468829 Solving 4.166666667 + x = 9.610468829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 9.610468829 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 9.610468829 + -4.166666667 x = 9.610468829 + -4.166666667 Combine like terms: 9.610468829 + -4.166666667 = 5.443802162 x = 5.443802162 Simplifying x = 5.443802162Subproblem 2
x + 4.166666667 = -9.610468829 Simplifying x + 4.166666667 = -9.610468829 Reorder the terms: 4.166666667 + x = -9.610468829 Solving 4.166666667 + x = -9.610468829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -9.610468829 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -9.610468829 + -4.166666667 x = -9.610468829 + -4.166666667 Combine like terms: -9.610468829 + -4.166666667 = -13.777135496 x = -13.777135496 Simplifying x = -13.777135496Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.443802162, -13.777135496}
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