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Simplifying -1x2 + 56x + 78 = 0 Reorder the terms: 78 + 56x + -1x2 = 0 Solving 78 + 56x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -78 + -56x + x2 = 0 Move the constant term to the right: Add '78' to each side of the equation. -78 + -56x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -56x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -56x + x2 = 0 + 78 -56x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -56x + x2 = 78 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = 78 + 784 Reorder the terms: 784 + -56x + x2 = 78 + 784 Combine like terms: 78 + 784 = 862 784 + -56x + x2 = 862 Factor a perfect square on the left side: (x + -28)(x + -28) = 862 Calculate the square root of the right side: 29.359836512 Break this problem into two subproblems by setting (x + -28) equal to 29.359836512 and -29.359836512.Subproblem 1
x + -28 = 29.359836512 Simplifying x + -28 = 29.359836512 Reorder the terms: -28 + x = 29.359836512 Solving -28 + x = 29.359836512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 29.359836512 + 28 Combine like terms: -28 + 28 = 0 0 + x = 29.359836512 + 28 x = 29.359836512 + 28 Combine like terms: 29.359836512 + 28 = 57.359836512 x = 57.359836512 Simplifying x = 57.359836512Subproblem 2
x + -28 = -29.359836512 Simplifying x + -28 = -29.359836512 Reorder the terms: -28 + x = -29.359836512 Solving -28 + x = -29.359836512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -29.359836512 + 28 Combine like terms: -28 + 28 = 0 0 + x = -29.359836512 + 28 x = -29.359836512 + 28 Combine like terms: -29.359836512 + 28 = -1.359836512 x = -1.359836512 Simplifying x = -1.359836512Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.359836512, -1.359836512}
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