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Simplifying 5x2 + 28x = 32 Reorder the terms: 28x + 5x2 = 32 Solving 28x + 5x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 28x + 5x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + 5.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 5.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 5.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 5.6x + x2 = 0 + 6.4 5.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 5.6x + x2 = 6.4 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 = 6.4 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 6.4 + 7.84 Combine like terms: 6.4 + 7.84 = 14.24 7.84 + 5.6x + x2 = 14.24 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 14.24 Calculate the square root of the right side: 3.773592453 Break this problem into two subproblems by setting (x + 2.8) equal to 3.773592453 and -3.773592453.Subproblem 1
x + 2.8 = 3.773592453 Simplifying x + 2.8 = 3.773592453 Reorder the terms: 2.8 + x = 3.773592453 Solving 2.8 + x = 3.773592453 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 = 3.773592453 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 3.773592453 + -2.8 x = 3.773592453 + -2.8 Combine like terms: 3.773592453 + -2.8 = 0.973592453 x = 0.973592453 Simplifying x = 0.973592453Subproblem 2
x + 2.8 = -3.773592453 Simplifying x + 2.8 = -3.773592453 Reorder the terms: 2.8 + x = -3.773592453 Solving 2.8 + x = -3.773592453 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 = -3.773592453 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -3.773592453 + -2.8 x = -3.773592453 + -2.8 Combine like terms: -3.773592453 + -2.8 = -6.573592453 x = -6.573592453 Simplifying x = -6.573592453Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.973592453, -6.573592453}
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