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Simplifying (x2 + -3) * 0.05 + -1(x + 3) * 0.05 = 0 Reorder the terms: (-3 + x2) * 0.05 + -1(x + 3) * 0.05 = 0 Reorder the terms for easier multiplication: 0.05(-3 + x2) + -1(x + 3) * 0.05 = 0 (-3 * 0.05 + x2 * 0.05) + -1(x + 3) * 0.05 = 0 (-0.15 + 0.05x2) + -1(x + 3) * 0.05 = 0 Reorder the terms: -0.15 + 0.05x2 + -1(3 + x) * 0.05 = 0 Reorder the terms for easier multiplication: -0.15 + 0.05x2 + -1 * 0.05(3 + x) = 0 Multiply -1 * 0.05 -0.15 + 0.05x2 + -0.05(3 + x) = 0 -0.15 + 0.05x2 + (3 * -0.05 + x * -0.05) = 0 -0.15 + 0.05x2 + (-0.15 + -0.05x) = 0 Reorder the terms: -0.15 + -0.15 + -0.05x + 0.05x2 = 0 Combine like terms: -0.15 + -0.15 = -0.3 -0.3 + -0.05x + 0.05x2 = 0 Solving -0.3 + -0.05x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -6 + -1x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x + x2 = 0 + 6 -1x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1x + x2 = 6 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 = 6 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6 + 0.25 Combine like terms: 6 + 0.25 = 6.25 0.25 + -1x + x2 = 6.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -0.5) equal to 2.5 and -2.5.Subproblem 1
x + -0.5 = 2.5 Simplifying x + -0.5 = 2.5 Reorder the terms: -0.5 + x = 2.5 Solving -0.5 + x = 2.5 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 = 2.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.5 + 0.5 x = 2.5 + 0.5 Combine like terms: 2.5 + 0.5 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -0.5 = -2.5 Simplifying x + -0.5 = -2.5 Reorder the terms: -0.5 + x = -2.5 Solving -0.5 + x = -2.5 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 = -2.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.5 + 0.5 x = -2.5 + 0.5 Combine like terms: -2.5 + 0.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -2}
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