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Simplifying (5x + 1)(x + -2) = 3 Reorder the terms: (1 + 5x)(x + -2) = 3 Reorder the terms: (1 + 5x)(-2 + x) = 3 Multiply (1 + 5x) * (-2 + x) (1(-2 + x) + 5x * (-2 + x)) = 3 ((-2 * 1 + x * 1) + 5x * (-2 + x)) = 3 ((-2 + 1x) + 5x * (-2 + x)) = 3 (-2 + 1x + (-2 * 5x + x * 5x)) = 3 (-2 + 1x + (-10x + 5x2)) = 3 Combine like terms: 1x + -10x = -9x (-2 + -9x + 5x2) = 3 Solving -2 + -9x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: -2 + -3 + -9x + 5x2 = 3 + -3 Combine like terms: -2 + -3 = -5 -5 + -9x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -5 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.8x + x2 = 0 + 1 -1.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.8x + x2 = 1 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 = 1 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1 + 0.81 Combine like terms: 1 + 0.81 = 1.81 0.81 + -1.8x + x2 = 1.81 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (x + -0.9) equal to 1.345362405 and -1.345362405.Subproblem 1
x + -0.9 = 1.345362405 Simplifying x + -0.9 = 1.345362405 Reorder the terms: -0.9 + x = 1.345362405 Solving -0.9 + x = 1.345362405 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 = 1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.345362405 + 0.9 x = 1.345362405 + 0.9 Combine like terms: 1.345362405 + 0.9 = 2.245362405 x = 2.245362405 Simplifying x = 2.245362405Subproblem 2
x + -0.9 = -1.345362405 Simplifying x + -0.9 = -1.345362405 Reorder the terms: -0.9 + x = -1.345362405 Solving -0.9 + x = -1.345362405 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 = -1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.345362405 + 0.9 x = -1.345362405 + 0.9 Combine like terms: -1.345362405 + 0.9 = -0.445362405 x = -0.445362405 Simplifying x = -0.445362405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.245362405, -0.445362405}
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