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Simplifying (x + -7)(4x + 1) = 7 Reorder the terms: (-7 + x)(4x + 1) = 7 Reorder the terms: (-7 + x)(1 + 4x) = 7 Multiply (-7 + x) * (1 + 4x) (-7(1 + 4x) + x(1 + 4x)) = 7 ((1 * -7 + 4x * -7) + x(1 + 4x)) = 7 ((-7 + -28x) + x(1 + 4x)) = 7 (-7 + -28x + (1 * x + 4x * x)) = 7 (-7 + -28x + (1x + 4x2)) = 7 Combine like terms: -28x + 1x = -27x (-7 + -27x + 4x2) = 7 Solving -7 + -27x + 4x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -7 + -27x + 4x2 = 7 + -7 Combine like terms: -7 + -7 = -14 -14 + -27x + 4x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -14 + -27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + -6.75x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -6.75x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -6.75x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -6.75x + x2 = 0 + 3.5 -6.75x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -6.75x + x2 = 3.5 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 3.5 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 3.5 + 11.390625 Combine like terms: 3.5 + 11.390625 = 14.890625 11.390625 + -6.75x + x2 = 14.890625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (x + -3.375) equal to 3.85883726 and -3.85883726.Subproblem 1
x + -3.375 = 3.85883726 Simplifying x + -3.375 = 3.85883726 Reorder the terms: -3.375 + x = 3.85883726 Solving -3.375 + x = 3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 3.85883726 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.85883726 + 3.375 x = 3.85883726 + 3.375 Combine like terms: 3.85883726 + 3.375 = 7.23383726 x = 7.23383726 Simplifying x = 7.23383726Subproblem 2
x + -3.375 = -3.85883726 Simplifying x + -3.375 = -3.85883726 Reorder the terms: -3.375 + x = -3.85883726 Solving -3.375 + x = -3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -3.85883726 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.85883726 + 3.375 x = -3.85883726 + 3.375 Combine like terms: -3.85883726 + 3.375 = -0.48383726 x = -0.48383726 Simplifying x = -0.48383726Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.23383726, -0.48383726}
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