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Simplifying 25x2 + -40x + -96 = 0 Reorder the terms: -96 + -40x + 25x2 = 0 Solving -96 + -40x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.84 + -1.6x + x2 = 0 Move the constant term to the right: Add '3.84' to each side of the equation. -3.84 + -1.6x + 3.84 + x2 = 0 + 3.84 Reorder the terms: -3.84 + 3.84 + -1.6x + x2 = 0 + 3.84 Combine like terms: -3.84 + 3.84 = 0.00 0.00 + -1.6x + x2 = 0 + 3.84 -1.6x + x2 = 0 + 3.84 Combine like terms: 0 + 3.84 = 3.84 -1.6x + x2 = 3.84 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 3.84 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 3.84 + 0.64 Combine like terms: 3.84 + 0.64 = 4.48 0.64 + -1.6x + x2 = 4.48 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 4.48 Calculate the square root of the right side: 2.116601049 Break this problem into two subproblems by setting (x + -0.8) equal to 2.116601049 and -2.116601049.Subproblem 1
x + -0.8 = 2.116601049 Simplifying x + -0.8 = 2.116601049 Reorder the terms: -0.8 + x = 2.116601049 Solving -0.8 + x = 2.116601049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.116601049 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.116601049 + 0.8 x = 2.116601049 + 0.8 Combine like terms: 2.116601049 + 0.8 = 2.916601049 x = 2.916601049 Simplifying x = 2.916601049Subproblem 2
x + -0.8 = -2.116601049 Simplifying x + -0.8 = -2.116601049 Reorder the terms: -0.8 + x = -2.116601049 Solving -0.8 + x = -2.116601049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.116601049 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.116601049 + 0.8 x = -2.116601049 + 0.8 Combine like terms: -2.116601049 + 0.8 = -1.316601049 x = -1.316601049 Simplifying x = -1.316601049Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.916601049, -1.316601049}
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