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Simplifying 5x2 + 26x + -22 = 0 Reorder the terms: -22 + 26x + 5x2 = 0 Solving -22 + 26x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + 5.2x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 5.2x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 5.2x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 5.2x + x2 = 0 + 4.4 5.2x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 5.2x + x2 = 4.4 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 4.4 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 4.4 + 6.76 Combine like terms: 4.4 + 6.76 = 11.16 6.76 + 5.2x + x2 = 11.16 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 11.16 Calculate the square root of the right side: 3.340658618 Break this problem into two subproblems by setting (x + 2.6) equal to 3.340658618 and -3.340658618.Subproblem 1
x + 2.6 = 3.340658618 Simplifying x + 2.6 = 3.340658618 Reorder the terms: 2.6 + x = 3.340658618 Solving 2.6 + x = 3.340658618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 3.340658618 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.340658618 + -2.6 x = 3.340658618 + -2.6 Combine like terms: 3.340658618 + -2.6 = 0.740658618 x = 0.740658618 Simplifying x = 0.740658618Subproblem 2
x + 2.6 = -3.340658618 Simplifying x + 2.6 = -3.340658618 Reorder the terms: 2.6 + x = -3.340658618 Solving 2.6 + x = -3.340658618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -3.340658618 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.340658618 + -2.6 x = -3.340658618 + -2.6 Combine like terms: -3.340658618 + -2.6 = -5.940658618 x = -5.940658618 Simplifying x = -5.940658618Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.740658618, -5.940658618}
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