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Simplifying 5x2 + -3x + -58 = -5 Reorder the terms: -58 + -3x + 5x2 = -5 Solving -58 + -3x + 5x2 = -5 Solving for variable 'x'. Reorder the terms: -58 + 5 + -3x + 5x2 = -5 + 5 Combine like terms: -58 + 5 = -53 -53 + -3x + 5x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -53 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.6 + -0.6x + x2 = 0 Move the constant term to the right: Add '10.6' to each side of the equation. -10.6 + -0.6x + 10.6 + x2 = 0 + 10.6 Reorder the terms: -10.6 + 10.6 + -0.6x + x2 = 0 + 10.6 Combine like terms: -10.6 + 10.6 = 0.0 0.0 + -0.6x + x2 = 0 + 10.6 -0.6x + x2 = 0 + 10.6 Combine like terms: 0 + 10.6 = 10.6 -0.6x + x2 = 10.6 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 10.6 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 10.6 + 0.09 Combine like terms: 10.6 + 0.09 = 10.69 0.09 + -0.6x + x2 = 10.69 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 10.69 Calculate the square root of the right side: 3.269556545 Break this problem into two subproblems by setting (x + -0.3) equal to 3.269556545 and -3.269556545.Subproblem 1
x + -0.3 = 3.269556545 Simplifying x + -0.3 = 3.269556545 Reorder the terms: -0.3 + x = 3.269556545 Solving -0.3 + x = 3.269556545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 3.269556545 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.269556545 + 0.3 x = 3.269556545 + 0.3 Combine like terms: 3.269556545 + 0.3 = 3.569556545 x = 3.569556545 Simplifying x = 3.569556545Subproblem 2
x + -0.3 = -3.269556545 Simplifying x + -0.3 = -3.269556545 Reorder the terms: -0.3 + x = -3.269556545 Solving -0.3 + x = -3.269556545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -3.269556545 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.269556545 + 0.3 x = -3.269556545 + 0.3 Combine like terms: -3.269556545 + 0.3 = -2.969556545 x = -2.969556545 Simplifying x = -2.969556545Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.569556545, -2.969556545}
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