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Simplifying 0 = -2.5x2 + 5.4x + 6.3 Reorder the terms: 0 = 6.3 + 5.4x + -2.5x2 Solving 0 = 6.3 + 5.4x + -2.5x2 Solving for variable 'x'. Combine like terms: 0 + -6.3 = -6.3 -6.3 + -5.4x + 2.5x2 = 6.3 + 5.4x + -2.5x2 + -6.3 + -5.4x + 2.5x2 Reorder the terms: -6.3 + -5.4x + 2.5x2 = 6.3 + -6.3 + 5.4x + -5.4x + -2.5x2 + 2.5x2 Combine like terms: 6.3 + -6.3 = 0.0 -6.3 + -5.4x + 2.5x2 = 0.0 + 5.4x + -5.4x + -2.5x2 + 2.5x2 -6.3 + -5.4x + 2.5x2 = 5.4x + -5.4x + -2.5x2 + 2.5x2 Combine like terms: 5.4x + -5.4x = 0.0 -6.3 + -5.4x + 2.5x2 = 0.0 + -2.5x2 + 2.5x2 -6.3 + -5.4x + 2.5x2 = -2.5x2 + 2.5x2 Combine like terms: -2.5x2 + 2.5x2 = 0.0 -6.3 + -5.4x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -2.52 + -2.16x + x2 = 0 Move the constant term to the right: Add '2.52' to each side of the equation. -2.52 + -2.16x + 2.52 + x2 = 0 + 2.52 Reorder the terms: -2.52 + 2.52 + -2.16x + x2 = 0 + 2.52 Combine like terms: -2.52 + 2.52 = 0.00 0.00 + -2.16x + x2 = 0 + 2.52 -2.16x + x2 = 0 + 2.52 Combine like terms: 0 + 2.52 = 2.52 -2.16x + x2 = 2.52 The x term is -2.16x. Take half its coefficient (-1.08). Square it (1.1664) and add it to both sides. Add '1.1664' to each side of the equation. -2.16x + 1.1664 + x2 = 2.52 + 1.1664 Reorder the terms: 1.1664 + -2.16x + x2 = 2.52 + 1.1664 Combine like terms: 2.52 + 1.1664 = 3.6864 1.1664 + -2.16x + x2 = 3.6864 Factor a perfect square on the left side: (x + -1.08)(x + -1.08) = 3.6864 Calculate the square root of the right side: 1.92 Break this problem into two subproblems by setting (x + -1.08) equal to 1.92 and -1.92.Subproblem 1
x + -1.08 = 1.92 Simplifying x + -1.08 = 1.92 Reorder the terms: -1.08 + x = 1.92 Solving -1.08 + x = 1.92 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.08' to each side of the equation. -1.08 + 1.08 + x = 1.92 + 1.08 Combine like terms: -1.08 + 1.08 = 0.00 0.00 + x = 1.92 + 1.08 x = 1.92 + 1.08 Combine like terms: 1.92 + 1.08 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.08 = -1.92 Simplifying x + -1.08 = -1.92 Reorder the terms: -1.08 + x = -1.92 Solving -1.08 + x = -1.92 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.08' to each side of the equation. -1.08 + 1.08 + x = -1.92 + 1.08 Combine like terms: -1.08 + 1.08 = 0.00 0.00 + x = -1.92 + 1.08 x = -1.92 + 1.08 Combine like terms: -1.92 + 1.08 = -0.84 x = -0.84 Simplifying x = -0.84Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -0.84}
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