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Simplifying 1.25x2 + -7x + 9 = 0 Reorder the terms: 9 + -7x + 1.25x2 = 0 Solving 9 + -7x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. 7.2 + -5.6x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -5.6x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -5.6x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -5.6x + x2 = 0 + -7.2 -5.6x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -5.6x + x2 = -7.2 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = -7.2 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = -7.2 + 7.84 Combine like terms: -7.2 + 7.84 = 0.64 7.84 + -5.6x + x2 = 0.64 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -2.8) equal to 0.8 and -0.8.Subproblem 1
x + -2.8 = 0.8 Simplifying x + -2.8 = 0.8 Reorder the terms: -2.8 + x = 0.8 Solving -2.8 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 0.8 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 0.8 + 2.8 x = 0.8 + 2.8 Combine like terms: 0.8 + 2.8 = 3.6 x = 3.6 Simplifying x = 3.6Subproblem 2
x + -2.8 = -0.8 Simplifying x + -2.8 = -0.8 Reorder the terms: -2.8 + x = -0.8 Solving -2.8 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -0.8 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -0.8 + 2.8 x = -0.8 + 2.8 Combine like terms: -0.8 + 2.8 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6, 2}
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