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Simplifying 0 = -3x2 + 14x + 200 Reorder the terms: 0 = 200 + 14x + -3x2 Solving 0 = 200 + 14x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + -14x + 3x2 = 200 + 14x + -3x2 + -200 + -14x + 3x2 Reorder the terms: -200 + -14x + 3x2 = 200 + -200 + 14x + -14x + -3x2 + 3x2 Combine like terms: 200 + -200 = 0 -200 + -14x + 3x2 = 0 + 14x + -14x + -3x2 + 3x2 -200 + -14x + 3x2 = 14x + -14x + -3x2 + 3x2 Combine like terms: 14x + -14x = 0 -200 + -14x + 3x2 = 0 + -3x2 + 3x2 -200 + -14x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -200 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -66.66666667 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '66.66666667' to each side of the equation. -66.66666667 + -4.666666667x + 66.66666667 + x2 = 0 + 66.66666667 Reorder the terms: -66.66666667 + 66.66666667 + -4.666666667x + x2 = 0 + 66.66666667 Combine like terms: -66.66666667 + 66.66666667 = 0.00000000 0.00000000 + -4.666666667x + x2 = 0 + 66.66666667 -4.666666667x + x2 = 0 + 66.66666667 Combine like terms: 0 + 66.66666667 = 66.66666667 -4.666666667x + x2 = 66.66666667 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 66.66666667 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 66.66666667 + 5.444444448 Combine like terms: 66.66666667 + 5.444444448 = 72.111111118 5.444444448 + -4.666666667x + x2 = 72.111111118 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 72.111111118 Calculate the square root of the right side: 8.491826136 Break this problem into two subproblems by setting (x + -2.333333334) equal to 8.491826136 and -8.491826136.Subproblem 1
x + -2.333333334 = 8.491826136 Simplifying x + -2.333333334 = 8.491826136 Reorder the terms: -2.333333334 + x = 8.491826136 Solving -2.333333334 + x = 8.491826136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 8.491826136 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 8.491826136 + 2.333333334 x = 8.491826136 + 2.333333334 Combine like terms: 8.491826136 + 2.333333334 = 10.82515947 x = 10.82515947 Simplifying x = 10.82515947Subproblem 2
x + -2.333333334 = -8.491826136 Simplifying x + -2.333333334 = -8.491826136 Reorder the terms: -2.333333334 + x = -8.491826136 Solving -2.333333334 + x = -8.491826136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -8.491826136 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -8.491826136 + 2.333333334 x = -8.491826136 + 2.333333334 Combine like terms: -8.491826136 + 2.333333334 = -6.158492802 x = -6.158492802 Simplifying x = -6.158492802Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.82515947, -6.158492802}
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