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Simplifying 19x2 + 16x + -76 = 0 Reorder the terms: -76 + 16x + 19x2 = 0 Solving -76 + 16x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -4 + 0.8421052632x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.8421052632x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.8421052632x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.8421052632x + x2 = 0 + 4 0.8421052632x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.8421052632x + x2 = 4 The x term is 0.8421052632x. Take half its coefficient (0.4210526316). Square it (0.1772853186) and add it to both sides. Add '0.1772853186' to each side of the equation. 0.8421052632x + 0.1772853186 + x2 = 4 + 0.1772853186 Reorder the terms: 0.1772853186 + 0.8421052632x + x2 = 4 + 0.1772853186 Combine like terms: 4 + 0.1772853186 = 4.1772853186 0.1772853186 + 0.8421052632x + x2 = 4.1772853186 Factor a perfect square on the left side: (x + 0.4210526316)(x + 0.4210526316) = 4.1772853186 Calculate the square root of the right side: 2.043840825 Break this problem into two subproblems by setting (x + 0.4210526316) equal to 2.043840825 and -2.043840825.Subproblem 1
x + 0.4210526316 = 2.043840825 Simplifying x + 0.4210526316 = 2.043840825 Reorder the terms: 0.4210526316 + x = 2.043840825 Solving 0.4210526316 + x = 2.043840825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4210526316' to each side of the equation. 0.4210526316 + -0.4210526316 + x = 2.043840825 + -0.4210526316 Combine like terms: 0.4210526316 + -0.4210526316 = 0.0000000000 0.0000000000 + x = 2.043840825 + -0.4210526316 x = 2.043840825 + -0.4210526316 Combine like terms: 2.043840825 + -0.4210526316 = 1.6227881934 x = 1.6227881934 Simplifying x = 1.6227881934Subproblem 2
x + 0.4210526316 = -2.043840825 Simplifying x + 0.4210526316 = -2.043840825 Reorder the terms: 0.4210526316 + x = -2.043840825 Solving 0.4210526316 + x = -2.043840825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4210526316' to each side of the equation. 0.4210526316 + -0.4210526316 + x = -2.043840825 + -0.4210526316 Combine like terms: 0.4210526316 + -0.4210526316 = 0.0000000000 0.0000000000 + x = -2.043840825 + -0.4210526316 x = -2.043840825 + -0.4210526316 Combine like terms: -2.043840825 + -0.4210526316 = -2.4648934566 x = -2.4648934566 Simplifying x = -2.4648934566Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6227881934, -2.4648934566}
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