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Simplifying 5x2 + 11x + -3 = 0 Reorder the terms: -3 + 11x + 5x2 = 0 Solving -3 + 11x + 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'. -0.6 + 2.2x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2.2x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2.2x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2.2x + x2 = 0 + 0.6 2.2x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2.2x + x2 = 0.6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 0.6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 0.6 + 1.21 Combine like terms: 0.6 + 1.21 = 1.81 1.21 + 2.2x + x2 = 1.81 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (x + 1.1) equal to 1.345362405 and -1.345362405.Subproblem 1
x + 1.1 = 1.345362405 Simplifying x + 1.1 = 1.345362405 Reorder the terms: 1.1 + x = 1.345362405 Solving 1.1 + x = 1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.345362405 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.345362405 + -1.1 x = 1.345362405 + -1.1 Combine like terms: 1.345362405 + -1.1 = 0.245362405 x = 0.245362405 Simplifying x = 0.245362405Subproblem 2
x + 1.1 = -1.345362405 Simplifying x + 1.1 = -1.345362405 Reorder the terms: 1.1 + x = -1.345362405 Solving 1.1 + x = -1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.345362405 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.345362405 + -1.1 x = -1.345362405 + -1.1 Combine like terms: -1.345362405 + -1.1 = -2.445362405 x = -2.445362405 Simplifying x = -2.445362405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.245362405, -2.445362405}
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