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Simplifying -12x + 3.75x2 = -9 Solving -12x + 3.75x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + -12x + 3.75x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -12x + 3.75x2 = 0 Begin completing the square. Divide all terms by 3.75 the coefficient of the squared term: Divide each side by '3.75'. 2.4 + -3.2x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -3.2x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -3.2x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -3.2x + x2 = 0 + -2.4 -3.2x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -3.2x + x2 = -2.4 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -2.4 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -2.4 + 2.56 Combine like terms: -2.4 + 2.56 = 0.16 2.56 + -3.2x + x2 = 0.16 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -1.6) equal to 0.4 and -0.4.Subproblem 1
x + -1.6 = 0.4 Simplifying x + -1.6 = 0.4 Reorder the terms: -1.6 + x = 0.4 Solving -1.6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 0.4 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 0.4 + 1.6 x = 0.4 + 1.6 Combine like terms: 0.4 + 1.6 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.6 = -0.4 Simplifying x + -1.6 = -0.4 Reorder the terms: -1.6 + x = -0.4 Solving -1.6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -0.4 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -0.4 + 1.6 x = -0.4 + 1.6 Combine like terms: -0.4 + 1.6 = 1.2 x = 1.2 Simplifying x = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 1.2}
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