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Simplifying 4x2 + 28x + 40 = x Reorder the terms: 40 + 28x + 4x2 = x Solving 40 + 28x + 4x2 = x Solving for variable 'x'. Reorder the terms: 40 + 28x + -1x + 4x2 = x + -1x Combine like terms: 28x + -1x = 27x 40 + 27x + 4x2 = x + -1x Combine like terms: x + -1x = 0 40 + 27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + 6.75x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 6.75x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 6.75x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 6.75x + x2 = 0 + -10 6.75x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 6.75x + x2 = -10 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 = -10 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -10 + 11.390625 Combine like terms: -10 + 11.390625 = 1.390625 11.390625 + 6.75x + x2 = 1.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + 3.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x + 3.375 = 1.179247642 Simplifying x + 3.375 = 1.179247642 Reorder the terms: 3.375 + x = 1.179247642 Solving 3.375 + x = 1.179247642 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 = 1.179247642 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 1.179247642 + -3.375 x = 1.179247642 + -3.375 Combine like terms: 1.179247642 + -3.375 = -2.195752358 x = -2.195752358 Simplifying x = -2.195752358Subproblem 2
x + 3.375 = -1.179247642 Simplifying x + 3.375 = -1.179247642 Reorder the terms: 3.375 + x = -1.179247642 Solving 3.375 + x = -1.179247642 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 = -1.179247642 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -1.179247642 + -3.375 x = -1.179247642 + -3.375 Combine like terms: -1.179247642 + -3.375 = -4.554247642 x = -4.554247642 Simplifying x = -4.554247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.195752358, -4.554247642}
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