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Simplifying -10x2 + 49x + -12 = 0 Reorder the terms: -12 + 49x + -10x2 = 0 Solving -12 + 49x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 1.2 + -4.9x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -4.9x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -4.9x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -4.9x + x2 = 0 + -1.2 -4.9x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -4.9x + x2 = -1.2 The x term is -4.9x. Take half its coefficient (-2.45). Square it (6.0025) and add it to both sides. Add '6.0025' to each side of the equation. -4.9x + 6.0025 + x2 = -1.2 + 6.0025 Reorder the terms: 6.0025 + -4.9x + x2 = -1.2 + 6.0025 Combine like terms: -1.2 + 6.0025 = 4.8025 6.0025 + -4.9x + x2 = 4.8025 Factor a perfect square on the left side: (x + -2.45)(x + -2.45) = 4.8025 Calculate the square root of the right side: 2.1914607 Break this problem into two subproblems by setting (x + -2.45) equal to 2.1914607 and -2.1914607.Subproblem 1
x + -2.45 = 2.1914607 Simplifying x + -2.45 = 2.1914607 Reorder the terms: -2.45 + x = 2.1914607 Solving -2.45 + x = 2.1914607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.45' to each side of the equation. -2.45 + 2.45 + x = 2.1914607 + 2.45 Combine like terms: -2.45 + 2.45 = 0.00 0.00 + x = 2.1914607 + 2.45 x = 2.1914607 + 2.45 Combine like terms: 2.1914607 + 2.45 = 4.6414607 x = 4.6414607 Simplifying x = 4.6414607Subproblem 2
x + -2.45 = -2.1914607 Simplifying x + -2.45 = -2.1914607 Reorder the terms: -2.45 + x = -2.1914607 Solving -2.45 + x = -2.1914607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.45' to each side of the equation. -2.45 + 2.45 + x = -2.1914607 + 2.45 Combine like terms: -2.45 + 2.45 = 0.00 0.00 + x = -2.1914607 + 2.45 x = -2.1914607 + 2.45 Combine like terms: -2.1914607 + 2.45 = 0.2585393 x = 0.2585393 Simplifying x = 0.2585393Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6414607, 0.2585393}
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