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Simplifying -4.9x2 + 12.5x + 150 = 0 Reorder the terms: 150 + 12.5x + -4.9x2 = 0 Solving 150 + 12.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -30.6122449 + -2.551020408x + x2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + -2.551020408x + 30.6122449 + x2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + -2.551020408x + x2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + -2.551020408x + x2 = 0 + 30.6122449 -2.551020408x + x2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 -2.551020408x + x2 = 30.6122449 The x term is -2.551020408x. Take half its coefficient (-1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. -2.551020408x + 1.626926281 + x2 = 30.6122449 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408x + x2 = 30.6122449 + 1.626926281 Combine like terms: 30.6122449 + 1.626926281 = 32.239171181 1.626926281 + -2.551020408x + x2 = 32.239171181 Factor a perfect square on the left side: (x + -1.275510204)(x + -1.275510204) = 32.239171181 Calculate the square root of the right side: 5.677954841 Break this problem into two subproblems by setting (x + -1.275510204) equal to 5.677954841 and -5.677954841.Subproblem 1
x + -1.275510204 = 5.677954841 Simplifying x + -1.275510204 = 5.677954841 Reorder the terms: -1.275510204 + x = 5.677954841 Solving -1.275510204 + x = 5.677954841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = 5.677954841 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = 5.677954841 + 1.275510204 x = 5.677954841 + 1.275510204 Combine like terms: 5.677954841 + 1.275510204 = 6.953465045 x = 6.953465045 Simplifying x = 6.953465045Subproblem 2
x + -1.275510204 = -5.677954841 Simplifying x + -1.275510204 = -5.677954841 Reorder the terms: -1.275510204 + x = -5.677954841 Solving -1.275510204 + x = -5.677954841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = -5.677954841 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = -5.677954841 + 1.275510204 x = -5.677954841 + 1.275510204 Combine like terms: -5.677954841 + 1.275510204 = -4.402444637 x = -4.402444637 Simplifying x = -4.402444637Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.953465045, -4.402444637}
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