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Simplifying 2 + -3(4 + -1x) = 5(2 + -1x) * 4x 2 + (4 * -3 + -1x * -3) = 5(2 + -1x) * 4x 2 + (-12 + 3x) = 5(2 + -1x) * 4x Combine like terms: 2 + -12 = -10 -10 + 3x = 5(2 + -1x) * 4x Reorder the terms for easier multiplication: -10 + 3x = 5 * 4x(2 + -1x) Multiply 5 * 4 -10 + 3x = 20x(2 + -1x) -10 + 3x = (2 * 20x + -1x * 20x) -10 + 3x = (40x + -20x2) Solving -10 + 3x = 40x + -20x2 Solving for variable 'x'. Combine like terms: 3x + -40x = -37x -10 + -37x + 20x2 = 40x + -20x2 + -40x + 20x2 Reorder the terms: -10 + -37x + 20x2 = 40x + -40x + -20x2 + 20x2 Combine like terms: 40x + -40x = 0 -10 + -37x + 20x2 = 0 + -20x2 + 20x2 -10 + -37x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -10 + -37x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.5 + -1.85x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.85x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.85x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.85x + x2 = 0 + 0.5 -1.85x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.85x + x2 = 0.5 The x term is -1.85x. Take half its coefficient (-0.925). Square it (0.855625) and add it to both sides. Add '0.855625' to each side of the equation. -1.85x + 0.855625 + x2 = 0.5 + 0.855625 Reorder the terms: 0.855625 + -1.85x + x2 = 0.5 + 0.855625 Combine like terms: 0.5 + 0.855625 = 1.355625 0.855625 + -1.85x + x2 = 1.355625 Factor a perfect square on the left side: (x + -0.925)(x + -0.925) = 1.355625 Calculate the square root of the right side: 1.164313102 Break this problem into two subproblems by setting (x + -0.925) equal to 1.164313102 and -1.164313102.Subproblem 1
x + -0.925 = 1.164313102 Simplifying x + -0.925 = 1.164313102 Reorder the terms: -0.925 + x = 1.164313102 Solving -0.925 + x = 1.164313102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = 1.164313102 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = 1.164313102 + 0.925 x = 1.164313102 + 0.925 Combine like terms: 1.164313102 + 0.925 = 2.089313102 x = 2.089313102 Simplifying x = 2.089313102Subproblem 2
x + -0.925 = -1.164313102 Simplifying x + -0.925 = -1.164313102 Reorder the terms: -0.925 + x = -1.164313102 Solving -0.925 + x = -1.164313102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = -1.164313102 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = -1.164313102 + 0.925 x = -1.164313102 + 0.925 Combine like terms: -1.164313102 + 0.925 = -0.239313102 x = -0.239313102 Simplifying x = -0.239313102Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.089313102, -0.239313102}
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