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Simplifying 1.8(0.25 + -1x) = x2 (0.25 * 1.8 + -1x * 1.8) = x2 (0.45 + -1.8x) = x2 Solving 0.45 + -1.8x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.45 + -1.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.45 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 1.8x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 1.8x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 1.8x + x2 = 0 + 0.45 1.8x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 1.8x + x2 = 0.45 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.45 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.45 + 0.81 Combine like terms: 0.45 + 0.81 = 1.26 0.81 + 1.8x + x2 = 1.26 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.26 Calculate the square root of the right side: 1.122497216 Break this problem into two subproblems by setting (x + 0.9) equal to 1.122497216 and -1.122497216.Subproblem 1
x + 0.9 = 1.122497216 Simplifying x + 0.9 = 1.122497216 Reorder the terms: 0.9 + x = 1.122497216 Solving 0.9 + x = 1.122497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.122497216 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.122497216 + -0.9 x = 1.122497216 + -0.9 Combine like terms: 1.122497216 + -0.9 = 0.222497216 x = 0.222497216 Simplifying x = 0.222497216Subproblem 2
x + 0.9 = -1.122497216 Simplifying x + 0.9 = -1.122497216 Reorder the terms: 0.9 + x = -1.122497216 Solving 0.9 + x = -1.122497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.122497216 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.122497216 + -0.9 x = -1.122497216 + -0.9 Combine like terms: -1.122497216 + -0.9 = -2.022497216 x = -2.022497216 Simplifying x = -2.022497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.222497216, -2.022497216}
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