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Simplifying 5x2 + 28x = 15 Reorder the terms: 28x + 5x2 = 15 Solving 28x + 5x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 28x + 5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 5.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.6x + x2 = 0 + 3 5.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.6x + x2 = 3 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = 3 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 3 + 7.84 Combine like terms: 3 + 7.84 = 10.84 7.84 + 5.6x + x2 = 10.84 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 10.84 Calculate the square root of the right side: 3.292415527 Break this problem into two subproblems by setting (x + 2.8) equal to 3.292415527 and -3.292415527.Subproblem 1
x + 2.8 = 3.292415527 Simplifying x + 2.8 = 3.292415527 Reorder the terms: 2.8 + x = 3.292415527 Solving 2.8 + x = 3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 3.292415527 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 3.292415527 + -2.8 x = 3.292415527 + -2.8 Combine like terms: 3.292415527 + -2.8 = 0.492415527 x = 0.492415527 Simplifying x = 0.492415527Subproblem 2
x + 2.8 = -3.292415527 Simplifying x + 2.8 = -3.292415527 Reorder the terms: 2.8 + x = -3.292415527 Solving 2.8 + x = -3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -3.292415527 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -3.292415527 + -2.8 x = -3.292415527 + -2.8 Combine like terms: -3.292415527 + -2.8 = -6.092415527 x = -6.092415527 Simplifying x = -6.092415527Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.492415527, -6.092415527}
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