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Simplifying 3x2 + 8x + -7500 = 0 Reorder the terms: -7500 + 8x + 3x2 = 0 Solving -7500 + 8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2500 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 2.666666667x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 2.666666667x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 2.666666667x + x2 = 0 + 2500 2.666666667x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 2.666666667x + x2 = 2500 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 2500 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 2500 + 1.777777780 Combine like terms: 2500 + 1.777777780 = 2501.77777778 1.777777780 + 2.666666667x + x2 = 2501.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2501.77777778 Calculate the square root of the right side: 50.017774618 Break this problem into two subproblems by setting (x + 1.333333334) equal to 50.017774618 and -50.017774618.Subproblem 1
x + 1.333333334 = 50.017774618 Simplifying x + 1.333333334 = 50.017774618 Reorder the terms: 1.333333334 + x = 50.017774618 Solving 1.333333334 + x = 50.017774618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 50.017774618 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 50.017774618 + -1.333333334 x = 50.017774618 + -1.333333334 Combine like terms: 50.017774618 + -1.333333334 = 48.684441284 x = 48.684441284 Simplifying x = 48.684441284Subproblem 2
x + 1.333333334 = -50.017774618 Simplifying x + 1.333333334 = -50.017774618 Reorder the terms: 1.333333334 + x = -50.017774618 Solving 1.333333334 + x = -50.017774618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -50.017774618 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -50.017774618 + -1.333333334 x = -50.017774618 + -1.333333334 Combine like terms: -50.017774618 + -1.333333334 = -51.351107952 x = -51.351107952 Simplifying x = -51.351107952Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.684441284, -51.351107952}
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