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Simplifying (4x + -7)(2x + 1) = 2x Reorder the terms: (-7 + 4x)(2x + 1) = 2x Reorder the terms: (-7 + 4x)(1 + 2x) = 2x Multiply (-7 + 4x) * (1 + 2x) (-7(1 + 2x) + 4x * (1 + 2x)) = 2x ((1 * -7 + 2x * -7) + 4x * (1 + 2x)) = 2x ((-7 + -14x) + 4x * (1 + 2x)) = 2x (-7 + -14x + (1 * 4x + 2x * 4x)) = 2x (-7 + -14x + (4x + 8x2)) = 2x Combine like terms: -14x + 4x = -10x (-7 + -10x + 8x2) = 2x Solving -7 + -10x + 8x2 = 2x Solving for variable 'x'. Reorder the terms: -7 + -10x + -2x + 8x2 = 2x + -2x Combine like terms: -10x + -2x = -12x -7 + -12x + 8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -7 + -12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -1.5x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -1.5x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -1.5x + x2 = 0 + 0.875 -1.5x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -1.5x + x2 = 0.875 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.875 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.875 + 0.5625 Combine like terms: 0.875 + 0.5625 = 1.4375 0.5625 + -1.5x + x2 = 1.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.4375 Calculate the square root of the right side: 1.198957881 Break this problem into two subproblems by setting (x + -0.75) equal to 1.198957881 and -1.198957881.Subproblem 1
x + -0.75 = 1.198957881 Simplifying x + -0.75 = 1.198957881 Reorder the terms: -0.75 + x = 1.198957881 Solving -0.75 + x = 1.198957881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.198957881 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.198957881 + 0.75 x = 1.198957881 + 0.75 Combine like terms: 1.198957881 + 0.75 = 1.948957881 x = 1.948957881 Simplifying x = 1.948957881Subproblem 2
x + -0.75 = -1.198957881 Simplifying x + -0.75 = -1.198957881 Reorder the terms: -0.75 + x = -1.198957881 Solving -0.75 + x = -1.198957881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.198957881 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.198957881 + 0.75 x = -1.198957881 + 0.75 Combine like terms: -1.198957881 + 0.75 = -0.448957881 x = -0.448957881 Simplifying x = -0.448957881Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.948957881, -0.448957881}
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