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Simplifying 4x2 + 40x + -19 = 0 Reorder the terms: -19 + 40x + 4x2 = 0 Solving -19 + 40x + 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 + 10x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 10x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 10x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 10x + x2 = 0 + 4.75 10x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 10x + x2 = 4.75 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 4.75 + 25 Reorder the terms: 25 + 10x + x2 = 4.75 + 25 Combine like terms: 4.75 + 25 = 29.75 25 + 10x + x2 = 29.75 Factor a perfect square on the left side: (x + 5)(x + 5) = 29.75 Calculate the square root of the right side: 5.454356057 Break this problem into two subproblems by setting (x + 5) equal to 5.454356057 and -5.454356057.Subproblem 1
x + 5 = 5.454356057 Simplifying x + 5 = 5.454356057 Reorder the terms: 5 + x = 5.454356057 Solving 5 + x = 5.454356057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.454356057 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.454356057 + -5 x = 5.454356057 + -5 Combine like terms: 5.454356057 + -5 = 0.454356057 x = 0.454356057 Simplifying x = 0.454356057Subproblem 2
x + 5 = -5.454356057 Simplifying x + 5 = -5.454356057 Reorder the terms: 5 + x = -5.454356057 Solving 5 + x = -5.454356057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.454356057 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.454356057 + -5 x = -5.454356057 + -5 Combine like terms: -5.454356057 + -5 = -10.454356057 x = -10.454356057 Simplifying x = -10.454356057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.454356057, -10.454356057}
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