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Simplifying 5x2 + 2x = 16 + -24x Reorder the terms: 2x + 5x2 = 16 + -24x Solving 2x + 5x2 = 16 + -24x Solving for variable 'x'. Reorder the terms: -16 + 2x + 24x + 5x2 = 16 + -24x + -16 + 24x Combine like terms: 2x + 24x = 26x -16 + 26x + 5x2 = 16 + -24x + -16 + 24x Reorder the terms: -16 + 26x + 5x2 = 16 + -16 + -24x + 24x Combine like terms: 16 + -16 = 0 -16 + 26x + 5x2 = 0 + -24x + 24x -16 + 26x + 5x2 = -24x + 24x Combine like terms: -24x + 24x = 0 -16 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 5.2x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 5.2x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 5.2x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 5.2x + x2 = 0 + 3.2 5.2x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 5.2x + x2 = 3.2 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 = 3.2 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 3.2 + 6.76 Combine like terms: 3.2 + 6.76 = 9.96 6.76 + 5.2x + x2 = 9.96 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (x + 2.6) equal to 3.155946768 and -3.155946768.Subproblem 1
x + 2.6 = 3.155946768 Simplifying x + 2.6 = 3.155946768 Reorder the terms: 2.6 + x = 3.155946768 Solving 2.6 + x = 3.155946768 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 = 3.155946768 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.155946768 + -2.6 x = 3.155946768 + -2.6 Combine like terms: 3.155946768 + -2.6 = 0.555946768 x = 0.555946768 Simplifying x = 0.555946768Subproblem 2
x + 2.6 = -3.155946768 Simplifying x + 2.6 = -3.155946768 Reorder the terms: 2.6 + x = -3.155946768 Solving 2.6 + x = -3.155946768 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 = -3.155946768 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.155946768 + -2.6 x = -3.155946768 + -2.6 Combine like terms: -3.155946768 + -2.6 = -5.755946768 x = -5.755946768 Simplifying x = -5.755946768Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.555946768, -5.755946768}
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