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Simplifying 5x2 + -23x + -16 = 0 Reorder the terms: -16 + -23x + 5x2 = 0 Solving -16 + -23x + 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'. -3.2 + -4.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -4.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -4.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -4.6x + x2 = 0 + 3.2 -4.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -4.6x + x2 = 3.2 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 3.2 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 3.2 + 5.29 Combine like terms: 3.2 + 5.29 = 8.49 5.29 + -4.6x + x2 = 8.49 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 8.49 Calculate the square root of the right side: 2.913760457 Break this problem into two subproblems by setting (x + -2.3) equal to 2.913760457 and -2.913760457.Subproblem 1
x + -2.3 = 2.913760457 Simplifying x + -2.3 = 2.913760457 Reorder the terms: -2.3 + x = 2.913760457 Solving -2.3 + x = 2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 2.913760457 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 2.913760457 + 2.3 x = 2.913760457 + 2.3 Combine like terms: 2.913760457 + 2.3 = 5.213760457 x = 5.213760457 Simplifying x = 5.213760457Subproblem 2
x + -2.3 = -2.913760457 Simplifying x + -2.3 = -2.913760457 Reorder the terms: -2.3 + x = -2.913760457 Solving -2.3 + x = -2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -2.913760457 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -2.913760457 + 2.3 x = -2.913760457 + 2.3 Combine like terms: -2.913760457 + 2.3 = -0.613760457 x = -0.613760457 Simplifying x = -0.613760457Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.213760457, -0.613760457}
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