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Simplifying x2 + 16 = 2x2 + -5x + -12 Reorder the terms: 16 + x2 = 2x2 + -5x + -12 Reorder the terms: 16 + x2 = -12 + -5x + 2x2 Solving 16 + x2 = -12 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 12 + 5x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2 Combine like terms: 16 + 12 = 28 28 + 5x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2 Combine like terms: x2 + -2x2 = -1x2 28 + 5x + -1x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2 Reorder the terms: 28 + 5x + -1x2 = -12 + 12 + -5x + 5x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 28 + 5x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2 28 + 5x + -1x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 28 + 5x + -1x2 = 0 + 2x2 + -2x2 28 + 5x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 28 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -5x + x2 = 0 + 28 -5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -5x + x2 = 28 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 28 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 28 + 6.25 Combine like terms: 28 + 6.25 = 34.25 6.25 + -5x + x2 = 34.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -2.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -2.5 = 5.852349955 Simplifying x + -2.5 = 5.852349955 Reorder the terms: -2.5 + x = 5.852349955 Solving -2.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.852349955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.852349955 + 2.5 x = 5.852349955 + 2.5 Combine like terms: 5.852349955 + 2.5 = 8.352349955 x = 8.352349955 Simplifying x = 8.352349955Subproblem 2
x + -2.5 = -5.852349955 Simplifying x + -2.5 = -5.852349955 Reorder the terms: -2.5 + x = -5.852349955 Solving -2.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.852349955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.852349955 + 2.5 x = -5.852349955 + 2.5 Combine like terms: -5.852349955 + 2.5 = -3.352349955 x = -3.352349955 Simplifying x = -3.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.352349955, -3.352349955}
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