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Simplifying 4x2 + -5x + -48 = 0 Reorder the terms: -48 + -5x + 4x2 = 0 Solving -48 + -5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12 + -1.25x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.25x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -1.25x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.25x + x2 = 0 + 12 -1.25x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.25x + x2 = 12 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 12 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 12 + 0.390625 Combine like terms: 12 + 0.390625 = 12.390625 0.390625 + -1.25x + x2 = 12.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (x + -0.625) equal to 3.52003196 and -3.52003196.Subproblem 1
x + -0.625 = 3.52003196 Simplifying x + -0.625 = 3.52003196 Reorder the terms: -0.625 + x = 3.52003196 Solving -0.625 + x = 3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 3.52003196 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.52003196 + 0.625 x = 3.52003196 + 0.625 Combine like terms: 3.52003196 + 0.625 = 4.14503196 x = 4.14503196 Simplifying x = 4.14503196Subproblem 2
x + -0.625 = -3.52003196 Simplifying x + -0.625 = -3.52003196 Reorder the terms: -0.625 + x = -3.52003196 Solving -0.625 + x = -3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -3.52003196 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.52003196 + 0.625 x = -3.52003196 + 0.625 Combine like terms: -3.52003196 + 0.625 = -2.89503196 x = -2.89503196 Simplifying x = -2.89503196Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.14503196, -2.89503196}
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