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Simplifying x + x2 = 0.78 Solving x + x2 = 0.78 Solving for variable 'x'. Reorder the terms: -0.78 + x + x2 = 0.78 + -0.78 Combine like terms: 0.78 + -0.78 = 0.00 -0.78 + x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.78' to each side of the equation. -0.78 + x + 0.78 + x2 = 0.00 + 0.78 Reorder the terms: -0.78 + 0.78 + x + x2 = 0.00 + 0.78 Combine like terms: -0.78 + 0.78 = 0.00 0.00 + x + x2 = 0.00 + 0.78 x + x2 = 0.00 + 0.78 Combine like terms: 0.00 + 0.78 = 0.78 x + x2 = 0.78 The x term is x. 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. x + 0.25 + x2 = 0.78 + 0.25 Reorder the terms: 0.25 + x + x2 = 0.78 + 0.25 Combine like terms: 0.78 + 0.25 = 1.03 0.25 + x + x2 = 1.03 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.03 Calculate the square root of the right side: 1.014889157 Break this problem into two subproblems by setting (x + 0.5) equal to 1.014889157 and -1.014889157.Subproblem 1
x + 0.5 = 1.014889157 Simplifying x + 0.5 = 1.014889157 Reorder the terms: 0.5 + x = 1.014889157 Solving 0.5 + x = 1.014889157 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 = 1.014889157 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.014889157 + -0.5 x = 1.014889157 + -0.5 Combine like terms: 1.014889157 + -0.5 = 0.514889157 x = 0.514889157 Simplifying x = 0.514889157Subproblem 2
x + 0.5 = -1.014889157 Simplifying x + 0.5 = -1.014889157 Reorder the terms: 0.5 + x = -1.014889157 Solving 0.5 + x = -1.014889157 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 = -1.014889157 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.014889157 + -0.5 x = -1.014889157 + -0.5 Combine like terms: -1.014889157 + -0.5 = -1.514889157 x = -1.514889157 Simplifying x = -1.514889157Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.514889157, -1.514889157}
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