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Simplifying 3x2 + -4x + -56 = x2 + 3x Reorder the terms: -56 + -4x + 3x2 = x2 + 3x Reorder the terms: -56 + -4x + 3x2 = 3x + x2 Solving -56 + -4x + 3x2 = 3x + x2 Solving for variable 'x'. Reorder the terms: -56 + -4x + -3x + 3x2 + -1x2 = 3x + x2 + -3x + -1x2 Combine like terms: -4x + -3x = -7x -56 + -7x + 3x2 + -1x2 = 3x + x2 + -3x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -56 + -7x + 2x2 = 3x + x2 + -3x + -1x2 Reorder the terms: -56 + -7x + 2x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -56 + -7x + 2x2 = 0 + x2 + -1x2 -56 + -7x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -56 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28 + -3.5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -3.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -3.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -3.5x + x2 = 0 + 28 -3.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -3.5x + x2 = 28 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 = 28 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 28 + 3.0625 Combine like terms: 28 + 3.0625 = 31.0625 3.0625 + -3.5x + x2 = 31.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (x + -1.75) equal to 5.573374202 and -5.573374202.Subproblem 1
x + -1.75 = 5.573374202 Simplifying x + -1.75 = 5.573374202 Reorder the terms: -1.75 + x = 5.573374202 Solving -1.75 + x = 5.573374202 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 = 5.573374202 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 5.573374202 + 1.75 x = 5.573374202 + 1.75 Combine like terms: 5.573374202 + 1.75 = 7.323374202 x = 7.323374202 Simplifying x = 7.323374202Subproblem 2
x + -1.75 = -5.573374202 Simplifying x + -1.75 = -5.573374202 Reorder the terms: -1.75 + x = -5.573374202 Solving -1.75 + x = -5.573374202 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 = -5.573374202 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -5.573374202 + 1.75 x = -5.573374202 + 1.75 Combine like terms: -5.573374202 + 1.75 = -3.823374202 x = -3.823374202 Simplifying x = -3.823374202Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.323374202, -3.823374202}
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