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Simplifying x2 + 4.5 + -7.5 = x + 7.5 Reorder the terms: 4.5 + -7.5 + x2 = x + 7.5 Combine like terms: 4.5 + -7.5 = -3 -3 + x2 = x + 7.5 Reorder the terms: -3 + x2 = 7.5 + x Solving -3 + x2 = 7.5 + x Solving for variable 'x'. Reorder the terms: -3 + -7.5 + -1x + x2 = 7.5 + x + -7.5 + -1x Combine like terms: -3 + -7.5 = -10.5 -10.5 + -1x + x2 = 7.5 + x + -7.5 + -1x Reorder the terms: -10.5 + -1x + x2 = 7.5 + -7.5 + x + -1x Combine like terms: 7.5 + -7.5 = 0.0 -10.5 + -1x + x2 = 0.0 + x + -1x -10.5 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -10.5 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -1x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -1x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -1x + x2 = 0 + 10.5 -1x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -1x + x2 = 10.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 10.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 10.5 + 0.25 Combine like terms: 10.5 + 0.25 = 10.75 0.25 + -1x + x2 = 10.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + -0.5) equal to 3.278719262 and -3.278719262.Subproblem 1
x + -0.5 = 3.278719262 Simplifying x + -0.5 = 3.278719262 Reorder the terms: -0.5 + x = 3.278719262 Solving -0.5 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.278719262 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.278719262 + 0.5 x = 3.278719262 + 0.5 Combine like terms: 3.278719262 + 0.5 = 3.778719262 x = 3.778719262 Simplifying x = 3.778719262Subproblem 2
x + -0.5 = -3.278719262 Simplifying x + -0.5 = -3.278719262 Reorder the terms: -0.5 + x = -3.278719262 Solving -0.5 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.278719262 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.278719262 + 0.5 x = -3.278719262 + 0.5 Combine like terms: -3.278719262 + 0.5 = -2.778719262 x = -2.778719262 Simplifying x = -2.778719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.778719262, -2.778719262}
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