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Simplifying 1.32x2 + -5x + -7000 = 0 Reorder the terms: -7000 + -5x + 1.32x2 = 0 Solving -7000 + -5x + 1.32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.32 the coefficient of the squared term: Divide each side by '1.32'. -5303.030303 + -3.787878788x + x2 = 0 Move the constant term to the right: Add '5303.030303' to each side of the equation. -5303.030303 + -3.787878788x + 5303.030303 + x2 = 0 + 5303.030303 Reorder the terms: -5303.030303 + 5303.030303 + -3.787878788x + x2 = 0 + 5303.030303 Combine like terms: -5303.030303 + 5303.030303 = 0.000000 0.000000 + -3.787878788x + x2 = 0 + 5303.030303 -3.787878788x + x2 = 0 + 5303.030303 Combine like terms: 0 + 5303.030303 = 5303.030303 -3.787878788x + x2 = 5303.030303 The x term is -3.787878788x. Take half its coefficient (-1.893939394). Square it (3.587006428) and add it to both sides. Add '3.587006428' to each side of the equation. -3.787878788x + 3.587006428 + x2 = 5303.030303 + 3.587006428 Reorder the terms: 3.587006428 + -3.787878788x + x2 = 5303.030303 + 3.587006428 Combine like terms: 5303.030303 + 3.587006428 = 5306.617309428 3.587006428 + -3.787878788x + x2 = 5306.617309428 Factor a perfect square on the left side: (x + -1.893939394)(x + -1.893939394) = 5306.617309428 Calculate the square root of the right side: 72.846532583 Break this problem into two subproblems by setting (x + -1.893939394) equal to 72.846532583 and -72.846532583.Subproblem 1
x + -1.893939394 = 72.846532583 Simplifying x + -1.893939394 = 72.846532583 Reorder the terms: -1.893939394 + x = 72.846532583 Solving -1.893939394 + x = 72.846532583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.893939394' to each side of the equation. -1.893939394 + 1.893939394 + x = 72.846532583 + 1.893939394 Combine like terms: -1.893939394 + 1.893939394 = 0.000000000 0.000000000 + x = 72.846532583 + 1.893939394 x = 72.846532583 + 1.893939394 Combine like terms: 72.846532583 + 1.893939394 = 74.740471977 x = 74.740471977 Simplifying x = 74.740471977Subproblem 2
x + -1.893939394 = -72.846532583 Simplifying x + -1.893939394 = -72.846532583 Reorder the terms: -1.893939394 + x = -72.846532583 Solving -1.893939394 + x = -72.846532583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.893939394' to each side of the equation. -1.893939394 + 1.893939394 + x = -72.846532583 + 1.893939394 Combine like terms: -1.893939394 + 1.893939394 = 0.000000000 0.000000000 + x = -72.846532583 + 1.893939394 x = -72.846532583 + 1.893939394 Combine like terms: -72.846532583 + 1.893939394 = -70.952593189 x = -70.952593189 Simplifying x = -70.952593189Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.740471977, -70.952593189}
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