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Simplifying 5x2 + -16x = 48 Reorder the terms: -16x + 5x2 = 48 Solving -16x + 5x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -16x + 5x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + -3.2x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -3.2x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -3.2x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -3.2x + x2 = 0 + 9.6 -3.2x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -3.2x + x2 = 9.6 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 9.6 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 9.6 + 2.56 Combine like terms: 9.6 + 2.56 = 12.16 2.56 + -3.2x + x2 = 12.16 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 12.16 Calculate the square root of the right side: 3.487119155 Break this problem into two subproblems by setting (x + -1.6) equal to 3.487119155 and -3.487119155.Subproblem 1
x + -1.6 = 3.487119155 Simplifying x + -1.6 = 3.487119155 Reorder the terms: -1.6 + x = 3.487119155 Solving -1.6 + x = 3.487119155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 3.487119155 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 3.487119155 + 1.6 x = 3.487119155 + 1.6 Combine like terms: 3.487119155 + 1.6 = 5.087119155 x = 5.087119155 Simplifying x = 5.087119155Subproblem 2
x + -1.6 = -3.487119155 Simplifying x + -1.6 = -3.487119155 Reorder the terms: -1.6 + x = -3.487119155 Solving -1.6 + x = -3.487119155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -3.487119155 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -3.487119155 + 1.6 x = -3.487119155 + 1.6 Combine like terms: -3.487119155 + 1.6 = -1.887119155 x = -1.887119155 Simplifying x = -1.887119155Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.087119155, -1.887119155}
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