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Simplifying 3x2 + 14x + 14x + 17 = 59 Reorder the terms: 17 + 14x + 14x + 3x2 = 59 Combine like terms: 14x + 14x = 28x 17 + 28x + 3x2 = 59 Solving 17 + 28x + 3x2 = 59 Solving for variable 'x'. Reorder the terms: 17 + -59 + 28x + 3x2 = 59 + -59 Combine like terms: 17 + -59 = -42 -42 + 28x + 3x2 = 59 + -59 Combine like terms: 59 + -59 = 0 -42 + 28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14 + 9.333333333x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 9.333333333x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 9.333333333x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9.333333333x + x2 = 0 + 14 9.333333333x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 9.333333333x + x2 = 14 The x term is 9.333333333x. Take half its coefficient (4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. 9.333333333x + 21.77777778 + x2 = 14 + 21.77777778 Reorder the terms: 21.77777778 + 9.333333333x + x2 = 14 + 21.77777778 Combine like terms: 14 + 21.77777778 = 35.77777778 21.77777778 + 9.333333333x + x2 = 35.77777778 Factor a perfect square on the left side: (x + 4.666666667)(x + 4.666666667) = 35.77777778 Calculate the square root of the right side: 5.981452815 Break this problem into two subproblems by setting (x + 4.666666667) equal to 5.981452815 and -5.981452815.Subproblem 1
x + 4.666666667 = 5.981452815 Simplifying x + 4.666666667 = 5.981452815 Reorder the terms: 4.666666667 + x = 5.981452815 Solving 4.666666667 + x = 5.981452815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = 5.981452815 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = 5.981452815 + -4.666666667 x = 5.981452815 + -4.666666667 Combine like terms: 5.981452815 + -4.666666667 = 1.314786148 x = 1.314786148 Simplifying x = 1.314786148Subproblem 2
x + 4.666666667 = -5.981452815 Simplifying x + 4.666666667 = -5.981452815 Reorder the terms: 4.666666667 + x = -5.981452815 Solving 4.666666667 + x = -5.981452815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = -5.981452815 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = -5.981452815 + -4.666666667 x = -5.981452815 + -4.666666667 Combine like terms: -5.981452815 + -4.666666667 = -10.648119482 x = -10.648119482 Simplifying x = -10.648119482Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.314786148, -10.648119482}
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