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Simplifying (4x + -2)(4x + -2) + -40x + -20 + 21 = 0 Reorder the terms: (-2 + 4x)(4x + -2) + -40x + -20 + 21 = 0 Reorder the terms: (-2 + 4x)(-2 + 4x) + -40x + -20 + 21 = 0 Multiply (-2 + 4x) * (-2 + 4x) (-2(-2 + 4x) + 4x * (-2 + 4x)) + -40x + -20 + 21 = 0 ((-2 * -2 + 4x * -2) + 4x * (-2 + 4x)) + -40x + -20 + 21 = 0 ((4 + -8x) + 4x * (-2 + 4x)) + -40x + -20 + 21 = 0 (4 + -8x + (-2 * 4x + 4x * 4x)) + -40x + -20 + 21 = 0 (4 + -8x + (-8x + 16x2)) + -40x + -20 + 21 = 0 Combine like terms: -8x + -8x = -16x (4 + -16x + 16x2) + -40x + -20 + 21 = 0 Reorder the terms: 4 + -20 + 21 + -16x + -40x + 16x2 = 0 Combine like terms: 4 + -20 = -16 -16 + 21 + -16x + -40x + 16x2 = 0 Combine like terms: -16 + 21 = 5 5 + -16x + -40x + 16x2 = 0 Combine like terms: -16x + -40x = -56x 5 + -56x + 16x2 = 0 Solving 5 + -56x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -3.5x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -3.5x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -3.5x + x2 = 0 + -0.3125 -3.5x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -3.5x + x2 = -0.3125 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.3125 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.3125 + 3.0625 Combine like terms: -0.3125 + 3.0625 = 2.75 3.0625 + -3.5x + x2 = 2.75 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -1.75) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -1.75 = 1.658312395 Simplifying x + -1.75 = 1.658312395 Reorder the terms: -1.75 + x = 1.658312395 Solving -1.75 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.658312395 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.658312395 + 1.75 x = 1.658312395 + 1.75 Combine like terms: 1.658312395 + 1.75 = 3.408312395 x = 3.408312395 Simplifying x = 3.408312395Subproblem 2
x + -1.75 = -1.658312395 Simplifying x + -1.75 = -1.658312395 Reorder the terms: -1.75 + x = -1.658312395 Solving -1.75 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.658312395 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.658312395 + 1.75 x = -1.658312395 + 1.75 Combine like terms: -1.658312395 + 1.75 = 0.091687605 x = 0.091687605 Simplifying x = 0.091687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.408312395, 0.091687605}
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