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Simplifying 48x2 + 153x + 62 = 0 Reorder the terms: 62 + 153x + 48x2 = 0 Solving 62 + 153x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 1.291666667 + 3.1875x + x2 = 0 Move the constant term to the right: Add '-1.291666667' to each side of the equation. 1.291666667 + 3.1875x + -1.291666667 + x2 = 0 + -1.291666667 Reorder the terms: 1.291666667 + -1.291666667 + 3.1875x + x2 = 0 + -1.291666667 Combine like terms: 1.291666667 + -1.291666667 = 0.000000000 0.000000000 + 3.1875x + x2 = 0 + -1.291666667 3.1875x + x2 = 0 + -1.291666667 Combine like terms: 0 + -1.291666667 = -1.291666667 3.1875x + x2 = -1.291666667 The x term is 3.1875x. Take half its coefficient (1.59375). Square it (2.540039063) and add it to both sides. Add '2.540039063' to each side of the equation. 3.1875x + 2.540039063 + x2 = -1.291666667 + 2.540039063 Reorder the terms: 2.540039063 + 3.1875x + x2 = -1.291666667 + 2.540039063 Combine like terms: -1.291666667 + 2.540039063 = 1.248372396 2.540039063 + 3.1875x + x2 = 1.248372396 Factor a perfect square on the left side: (x + 1.59375)(x + 1.59375) = 1.248372396 Calculate the square root of the right side: 1.117305865 Break this problem into two subproblems by setting (x + 1.59375) equal to 1.117305865 and -1.117305865.Subproblem 1
x + 1.59375 = 1.117305865 Simplifying x + 1.59375 = 1.117305865 Reorder the terms: 1.59375 + x = 1.117305865 Solving 1.59375 + x = 1.117305865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.59375' to each side of the equation. 1.59375 + -1.59375 + x = 1.117305865 + -1.59375 Combine like terms: 1.59375 + -1.59375 = 0.00000 0.00000 + x = 1.117305865 + -1.59375 x = 1.117305865 + -1.59375 Combine like terms: 1.117305865 + -1.59375 = -0.476444135 x = -0.476444135 Simplifying x = -0.476444135Subproblem 2
x + 1.59375 = -1.117305865 Simplifying x + 1.59375 = -1.117305865 Reorder the terms: 1.59375 + x = -1.117305865 Solving 1.59375 + x = -1.117305865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.59375' to each side of the equation. 1.59375 + -1.59375 + x = -1.117305865 + -1.59375 Combine like terms: 1.59375 + -1.59375 = 0.00000 0.00000 + x = -1.117305865 + -1.59375 x = -1.117305865 + -1.59375 Combine like terms: -1.117305865 + -1.59375 = -2.711055865 x = -2.711055865 Simplifying x = -2.711055865Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.476444135, -2.711055865}
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