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Simplifying 4x2 + 24x + -19 = 0 Reorder the terms: -19 + 24x + 4x2 = 0 Solving -19 + 24x + 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'. -4.75 + 6x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 6x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 6x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 6x + x2 = 0 + 4.75 6x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 6x + x2 = 4.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 4.75 + 9 Reorder the terms: 9 + 6x + x2 = 4.75 + 9 Combine like terms: 4.75 + 9 = 13.75 9 + 6x + x2 = 13.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + 3) equal to 3.708099244 and -3.708099244.Subproblem 1
x + 3 = 3.708099244 Simplifying x + 3 = 3.708099244 Reorder the terms: 3 + x = 3.708099244 Solving 3 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.708099244 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.708099244 + -3 x = 3.708099244 + -3 Combine like terms: 3.708099244 + -3 = 0.708099244 x = 0.708099244 Simplifying x = 0.708099244Subproblem 2
x + 3 = -3.708099244 Simplifying x + 3 = -3.708099244 Reorder the terms: 3 + x = -3.708099244 Solving 3 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.708099244 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.708099244 + -3 x = -3.708099244 + -3 Combine like terms: -3.708099244 + -3 = -6.708099244 x = -6.708099244 Simplifying x = -6.708099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.708099244, -6.708099244}
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