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Simplifying 4x2 + -15x + -97 = 0 Reorder the terms: -97 + -15x + 4x2 = 0 Solving -97 + -15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -24.25 + -3.75x + x2 = 0 Move the constant term to the right: Add '24.25' to each side of the equation. -24.25 + -3.75x + 24.25 + x2 = 0 + 24.25 Reorder the terms: -24.25 + 24.25 + -3.75x + x2 = 0 + 24.25 Combine like terms: -24.25 + 24.25 = 0.00 0.00 + -3.75x + x2 = 0 + 24.25 -3.75x + x2 = 0 + 24.25 Combine like terms: 0 + 24.25 = 24.25 -3.75x + x2 = 24.25 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 24.25 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 24.25 + 3.515625 Combine like terms: 24.25 + 3.515625 = 27.765625 3.515625 + -3.75x + x2 = 27.765625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 27.765625 Calculate the square root of the right side: 5.269309727 Break this problem into two subproblems by setting (x + -1.875) equal to 5.269309727 and -5.269309727.Subproblem 1
x + -1.875 = 5.269309727 Simplifying x + -1.875 = 5.269309727 Reorder the terms: -1.875 + x = 5.269309727 Solving -1.875 + x = 5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 5.269309727 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 5.269309727 + 1.875 x = 5.269309727 + 1.875 Combine like terms: 5.269309727 + 1.875 = 7.144309727 x = 7.144309727 Simplifying x = 7.144309727Subproblem 2
x + -1.875 = -5.269309727 Simplifying x + -1.875 = -5.269309727 Reorder the terms: -1.875 + x = -5.269309727 Solving -1.875 + x = -5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -5.269309727 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -5.269309727 + 1.875 x = -5.269309727 + 1.875 Combine like terms: -5.269309727 + 1.875 = -3.394309727 x = -3.394309727 Simplifying x = -3.394309727Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.144309727, -3.394309727}
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