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Simplifying 0.4(x2 + 1) = x Reorder the terms: 0.4(1 + x2) = x (1 * 0.4 + x2 * 0.4) = x (0.4 + 0.4x2) = x Solving 0.4 + 0.4x2 = x Solving for variable 'x'. Reorder the terms: 0.4 + -1x + 0.4x2 = x + -1x Combine like terms: x + -1x = 0 0.4 + -1x + 0.4x2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 1 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.5x + x2 = 0 + -1 -2.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.5x + x2 = -1 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1 + 1.5625 Combine like terms: -1 + 1.5625 = 0.5625 1.5625 + -2.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + -1.25) equal to 0.75 and -0.75.Subproblem 1
x + -1.25 = 0.75 Simplifying x + -1.25 = 0.75 Reorder the terms: -1.25 + x = 0.75 Solving -1.25 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.75 + 1.25 x = 0.75 + 1.25 Combine like terms: 0.75 + 1.25 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.25 = -0.75 Simplifying x + -1.25 = -0.75 Reorder the terms: -1.25 + x = -0.75 Solving -1.25 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.75 + 1.25 x = -0.75 + 1.25 Combine like terms: -0.75 + 1.25 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 0.5}
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