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Simplifying 49 + 89x + 38x2 = 0 Solving 49 + 89x + 38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. 1.289473684 + 2.342105263x + x2 = 0 Move the constant term to the right: Add '-1.289473684' to each side of the equation. 1.289473684 + 2.342105263x + -1.289473684 + x2 = 0 + -1.289473684 Reorder the terms: 1.289473684 + -1.289473684 + 2.342105263x + x2 = 0 + -1.289473684 Combine like terms: 1.289473684 + -1.289473684 = 0.000000000 0.000000000 + 2.342105263x + x2 = 0 + -1.289473684 2.342105263x + x2 = 0 + -1.289473684 Combine like terms: 0 + -1.289473684 = -1.289473684 2.342105263x + x2 = -1.289473684 The x term is 2.342105263x. Take half its coefficient (1.171052632). Square it (1.371364267) and add it to both sides. Add '1.371364267' to each side of the equation. 2.342105263x + 1.371364267 + x2 = -1.289473684 + 1.371364267 Reorder the terms: 1.371364267 + 2.342105263x + x2 = -1.289473684 + 1.371364267 Combine like terms: -1.289473684 + 1.371364267 = 0.081890583 1.371364267 + 2.342105263x + x2 = 0.081890583 Factor a perfect square on the left side: (x + 1.171052632)(x + 1.171052632) = 0.081890583 Calculate the square root of the right side: 0.286165307 Break this problem into two subproblems by setting (x + 1.171052632) equal to 0.286165307 and -0.286165307.Subproblem 1
x + 1.171052632 = 0.286165307 Simplifying x + 1.171052632 = 0.286165307 Reorder the terms: 1.171052632 + x = 0.286165307 Solving 1.171052632 + x = 0.286165307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.171052632' to each side of the equation. 1.171052632 + -1.171052632 + x = 0.286165307 + -1.171052632 Combine like terms: 1.171052632 + -1.171052632 = 0.000000000 0.000000000 + x = 0.286165307 + -1.171052632 x = 0.286165307 + -1.171052632 Combine like terms: 0.286165307 + -1.171052632 = -0.884887325 x = -0.884887325 Simplifying x = -0.884887325Subproblem 2
x + 1.171052632 = -0.286165307 Simplifying x + 1.171052632 = -0.286165307 Reorder the terms: 1.171052632 + x = -0.286165307 Solving 1.171052632 + x = -0.286165307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.171052632' to each side of the equation. 1.171052632 + -1.171052632 + x = -0.286165307 + -1.171052632 Combine like terms: 1.171052632 + -1.171052632 = 0.000000000 0.000000000 + x = -0.286165307 + -1.171052632 x = -0.286165307 + -1.171052632 Combine like terms: -0.286165307 + -1.171052632 = -1.457217939 x = -1.457217939 Simplifying x = -1.457217939Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.884887325, -1.457217939}
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