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Simplifying x(5x + 1) = 4x + -4x + 28 Reorder the terms: x(1 + 5x) = 4x + -4x + 28 (1 * x + 5x * x) = 4x + -4x + 28 (1x + 5x2) = 4x + -4x + 28 Reorder the terms: 1x + 5x2 = 28 + 4x + -4x Combine like terms: 4x + -4x = 0 1x + 5x2 = 28 + 0 1x + 5x2 = 28 Solving 1x + 5x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 1x + 5x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + 0.2x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 0.2x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 0.2x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 0.2x + x2 = 0 + 5.6 0.2x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 0.2x + x2 = 5.6 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 5.6 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 5.6 + 0.01 Combine like terms: 5.6 + 0.01 = 5.61 0.01 + 0.2x + x2 = 5.61 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 5.61 Calculate the square root of the right side: 2.368543856 Break this problem into two subproblems by setting (x + 0.1) equal to 2.368543856 and -2.368543856.Subproblem 1
x + 0.1 = 2.368543856 Simplifying x + 0.1 = 2.368543856 Reorder the terms: 0.1 + x = 2.368543856 Solving 0.1 + x = 2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.368543856 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.368543856 + -0.1 x = 2.368543856 + -0.1 Combine like terms: 2.368543856 + -0.1 = 2.268543856 x = 2.268543856 Simplifying x = 2.268543856Subproblem 2
x + 0.1 = -2.368543856 Simplifying x + 0.1 = -2.368543856 Reorder the terms: 0.1 + x = -2.368543856 Solving 0.1 + x = -2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.368543856 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.368543856 + -0.1 x = -2.368543856 + -0.1 Combine like terms: -2.368543856 + -0.1 = -2.468543856 x = -2.468543856 Simplifying x = -2.468543856Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.268543856, -2.468543856}
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