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Simplifying 6.25x2 + -90x + -56.25 = 0 Reorder the terms: -56.25 + -90x + 6.25x2 = 0 Solving -56.25 + -90x + 6.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.25 the coefficient of the squared term: Divide each side by '6.25'. -9 + -14.4x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -14.4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -14.4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14.4x + x2 = 0 + 9 -14.4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -14.4x + x2 = 9 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = 9 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 9 + 51.84 Combine like terms: 9 + 51.84 = 60.84 51.84 + -14.4x + x2 = 60.84 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 60.84 Calculate the square root of the right side: 7.8 Break this problem into two subproblems by setting (x + -7.2) equal to 7.8 and -7.8.Subproblem 1
x + -7.2 = 7.8 Simplifying x + -7.2 = 7.8 Reorder the terms: -7.2 + x = 7.8 Solving -7.2 + x = 7.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 7.8 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 7.8 + 7.2 x = 7.8 + 7.2 Combine like terms: 7.8 + 7.2 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -7.2 = -7.8 Simplifying x + -7.2 = -7.8 Reorder the terms: -7.2 + x = -7.8 Solving -7.2 + x = -7.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -7.8 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -7.8 + 7.2 x = -7.8 + 7.2 Combine like terms: -7.8 + 7.2 = -0.6 x = -0.6 Simplifying x = -0.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -0.6}
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