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Simplifying 5x2 + -56x + 36 = 0 Reorder the terms: 36 + -56x + 5x2 = 0 Solving 36 + -56x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -11.2x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -11.2x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -11.2x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -11.2x + x2 = 0 + -7.2 -11.2x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -11.2x + x2 = -7.2 The x term is -11.2x. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2x + 31.36 + x2 = -7.2 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = -7.2 + 31.36 Combine like terms: -7.2 + 31.36 = 24.16 31.36 + -11.2x + x2 = 24.16 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 24.16 Calculate the square root of the right side: 4.915282291 Break this problem into two subproblems by setting (x + -5.6) equal to 4.915282291 and -4.915282291.Subproblem 1
x + -5.6 = 4.915282291 Simplifying x + -5.6 = 4.915282291 Reorder the terms: -5.6 + x = 4.915282291 Solving -5.6 + x = 4.915282291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = 4.915282291 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 4.915282291 + 5.6 x = 4.915282291 + 5.6 Combine like terms: 4.915282291 + 5.6 = 10.515282291 x = 10.515282291 Simplifying x = 10.515282291Subproblem 2
x + -5.6 = -4.915282291 Simplifying x + -5.6 = -4.915282291 Reorder the terms: -5.6 + x = -4.915282291 Solving -5.6 + x = -4.915282291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = -4.915282291 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -4.915282291 + 5.6 x = -4.915282291 + 5.6 Combine like terms: -4.915282291 + 5.6 = 0.684717709 x = 0.684717709 Simplifying x = 0.684717709Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.515282291, 0.684717709}
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