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Simplifying -5x2 + 20x + 14 = 25 Reorder the terms: 14 + 20x + -5x2 = 25 Solving 14 + 20x + -5x2 = 25 Solving for variable 'x'. Reorder the terms: 14 + -25 + 20x + -5x2 = 25 + -25 Combine like terms: 14 + -25 = -11 -11 + 20x + -5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -11 + 20x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.2 + -4x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -4x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -4x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -4x + x2 = 0 + -2.2 -4x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -4x + x2 = -2.2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.2 + 4 Reorder the terms: 4 + -4x + x2 = -2.2 + 4 Combine like terms: -2.2 + 4 = 1.8 4 + -4x + x2 = 1.8 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + -2) equal to 1.341640787 and -1.341640787.Subproblem 1
x + -2 = 1.341640787 Simplifying x + -2 = 1.341640787 Reorder the terms: -2 + x = 1.341640787 Solving -2 + x = 1.341640787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.341640787 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.341640787 + 2 x = 1.341640787 + 2 Combine like terms: 1.341640787 + 2 = 3.341640787 x = 3.341640787 Simplifying x = 3.341640787Subproblem 2
x + -2 = -1.341640787 Simplifying x + -2 = -1.341640787 Reorder the terms: -2 + x = -1.341640787 Solving -2 + x = -1.341640787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.341640787 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.341640787 + 2 x = -1.341640787 + 2 Combine like terms: -1.341640787 + 2 = 0.658359213 x = 0.658359213 Simplifying x = 0.658359213Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.341640787, 0.658359213}
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