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Simplifying 5x2 + 16x + -6 = 3 Reorder the terms: -6 + 16x + 5x2 = 3 Solving -6 + 16x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: -6 + -3 + 16x + 5x2 = 3 + -3 Combine like terms: -6 + -3 = -9 -9 + 16x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -9 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 3.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 3.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 3.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 3.2x + x2 = 0 + 1.8 3.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 3.2x + x2 = 1.8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 1.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 1.8 + 2.56 Combine like terms: 1.8 + 2.56 = 4.36 2.56 + 3.2x + x2 = 4.36 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + 1.6) equal to 2.088061302 and -2.088061302.Subproblem 1
x + 1.6 = 2.088061302 Simplifying x + 1.6 = 2.088061302 Reorder the terms: 1.6 + x = 2.088061302 Solving 1.6 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 2.088061302 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 2.088061302 + -1.6 x = 2.088061302 + -1.6 Combine like terms: 2.088061302 + -1.6 = 0.488061302 x = 0.488061302 Simplifying x = 0.488061302Subproblem 2
x + 1.6 = -2.088061302 Simplifying x + 1.6 = -2.088061302 Reorder the terms: 1.6 + x = -2.088061302 Solving 1.6 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -2.088061302 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -2.088061302 + -1.6 x = -2.088061302 + -1.6 Combine like terms: -2.088061302 + -1.6 = -3.688061302 x = -3.688061302 Simplifying x = -3.688061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.488061302, -3.688061302}
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