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Simplifying x2 + 8x + 152x = 3x2 + 5x + -7 Reorder the terms: 8x + 152x + x2 = 3x2 + 5x + -7 Combine like terms: 8x + 152x = 160x 160x + x2 = 3x2 + 5x + -7 Reorder the terms: 160x + x2 = -7 + 5x + 3x2 Solving 160x + x2 = -7 + 5x + 3x2 Solving for variable 'x'. Reorder the terms: 7 + 160x + -5x + x2 + -3x2 = -7 + 5x + 3x2 + 7 + -5x + -3x2 Combine like terms: 160x + -5x = 155x 7 + 155x + x2 + -3x2 = -7 + 5x + 3x2 + 7 + -5x + -3x2 Combine like terms: x2 + -3x2 = -2x2 7 + 155x + -2x2 = -7 + 5x + 3x2 + 7 + -5x + -3x2 Reorder the terms: 7 + 155x + -2x2 = -7 + 7 + 5x + -5x + 3x2 + -3x2 Combine like terms: -7 + 7 = 0 7 + 155x + -2x2 = 0 + 5x + -5x + 3x2 + -3x2 7 + 155x + -2x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 7 + 155x + -2x2 = 0 + 3x2 + -3x2 7 + 155x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 7 + 155x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -77.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -77.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -77.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -77.5x + x2 = 0 + 3.5 -77.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -77.5x + x2 = 3.5 The x term is -77.5x. Take half its coefficient (-38.75). Square it (1501.5625) and add it to both sides. Add '1501.5625' to each side of the equation. -77.5x + 1501.5625 + x2 = 3.5 + 1501.5625 Reorder the terms: 1501.5625 + -77.5x + x2 = 3.5 + 1501.5625 Combine like terms: 3.5 + 1501.5625 = 1505.0625 1501.5625 + -77.5x + x2 = 1505.0625 Factor a perfect square on the left side: (x + -38.75)(x + -38.75) = 1505.0625 Calculate the square root of the right side: 38.795135004 Break this problem into two subproblems by setting (x + -38.75) equal to 38.795135004 and -38.795135004.Subproblem 1
x + -38.75 = 38.795135004 Simplifying x + -38.75 = 38.795135004 Reorder the terms: -38.75 + x = 38.795135004 Solving -38.75 + x = 38.795135004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.75' to each side of the equation. -38.75 + 38.75 + x = 38.795135004 + 38.75 Combine like terms: -38.75 + 38.75 = 0.00 0.00 + x = 38.795135004 + 38.75 x = 38.795135004 + 38.75 Combine like terms: 38.795135004 + 38.75 = 77.545135004 x = 77.545135004 Simplifying x = 77.545135004Subproblem 2
x + -38.75 = -38.795135004 Simplifying x + -38.75 = -38.795135004 Reorder the terms: -38.75 + x = -38.795135004 Solving -38.75 + x = -38.795135004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.75' to each side of the equation. -38.75 + 38.75 + x = -38.795135004 + 38.75 Combine like terms: -38.75 + 38.75 = 0.00 0.00 + x = -38.795135004 + 38.75 x = -38.795135004 + 38.75 Combine like terms: -38.795135004 + 38.75 = -0.045135004 x = -0.045135004 Simplifying x = -0.045135004Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.545135004, -0.045135004}
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