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Simplifying x2 + -4x = x + 1.89 Reorder the terms: -4x + x2 = x + 1.89 Reorder the terms: -4x + x2 = 1.89 + x Solving -4x + x2 = 1.89 + x Solving for variable 'x'. Reorder the terms: -1.89 + -4x + -1x + x2 = 1.89 + x + -1.89 + -1x Combine like terms: -4x + -1x = -5x -1.89 + -5x + x2 = 1.89 + x + -1.89 + -1x Reorder the terms: -1.89 + -5x + x2 = 1.89 + -1.89 + x + -1x Combine like terms: 1.89 + -1.89 = 0.00 -1.89 + -5x + x2 = 0.00 + x + -1x -1.89 + -5x + x2 = x + -1x Combine like terms: x + -1x = 0 -1.89 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1.89' to each side of the equation. -1.89 + -5x + 1.89 + x2 = 0 + 1.89 Reorder the terms: -1.89 + 1.89 + -5x + x2 = 0 + 1.89 Combine like terms: -1.89 + 1.89 = 0.00 0.00 + -5x + x2 = 0 + 1.89 -5x + x2 = 0 + 1.89 Combine like terms: 0 + 1.89 = 1.89 -5x + x2 = 1.89 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 = 1.89 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.89 + 6.25 Combine like terms: 1.89 + 6.25 = 8.14 6.25 + -5x + x2 = 8.14 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.14 Calculate the square root of the right side: 2.853068524 Break this problem into two subproblems by setting (x + -2.5) equal to 2.853068524 and -2.853068524.Subproblem 1
x + -2.5 = 2.853068524 Simplifying x + -2.5 = 2.853068524 Reorder the terms: -2.5 + x = 2.853068524 Solving -2.5 + x = 2.853068524 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 = 2.853068524 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.853068524 + 2.5 x = 2.853068524 + 2.5 Combine like terms: 2.853068524 + 2.5 = 5.353068524 x = 5.353068524 Simplifying x = 5.353068524Subproblem 2
x + -2.5 = -2.853068524 Simplifying x + -2.5 = -2.853068524 Reorder the terms: -2.5 + x = -2.853068524 Solving -2.5 + x = -2.853068524 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 = -2.853068524 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.853068524 + 2.5 x = -2.853068524 + 2.5 Combine like terms: -2.853068524 + 2.5 = -0.353068524 x = -0.353068524 Simplifying x = -0.353068524Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.353068524, -0.353068524}
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