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Simplifying 14x = 2x2 + 15 Reorder the terms: 14x = 15 + 2x2 Solving 14x = 15 + 2x2 Solving for variable 'x'. Reorder the terms: -15 + 14x + -2x2 = 15 + 2x2 + -15 + -2x2 Reorder the terms: -15 + 14x + -2x2 = 15 + -15 + 2x2 + -2x2 Combine like terms: 15 + -15 = 0 -15 + 14x + -2x2 = 0 + 2x2 + -2x2 -15 + 14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + 14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -7x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7x + x2 = 0 + -7.5 -7x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7x + x2 = -7.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -7.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -7.5 + 12.25 Combine like terms: -7.5 + 12.25 = 4.75 12.25 + -7x + x2 = 4.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -3.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -3.5 = 2.179449472 Simplifying x + -3.5 = 2.179449472 Reorder the terms: -3.5 + x = 2.179449472 Solving -3.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.179449472 + 3.5 x = 2.179449472 + 3.5 Combine like terms: 2.179449472 + 3.5 = 5.679449472 x = 5.679449472 Simplifying x = 5.679449472Subproblem 2
x + -3.5 = -2.179449472 Simplifying x + -3.5 = -2.179449472 Reorder the terms: -3.5 + x = -2.179449472 Solving -3.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.179449472 + 3.5 x = -2.179449472 + 3.5 Combine like terms: -2.179449472 + 3.5 = 1.320550528 x = 1.320550528 Simplifying x = 1.320550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.679449472, 1.320550528}
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