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Simplifying 14x + 3.5x2 = 15 Solving 14x + 3.5x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 14x + 3.5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 14x + 3.5x2 = 0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -4.285714286 + 4x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 4x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 4x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 4x + x2 = 0 + 4.285714286 4x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 4x + x2 = 4.285714286 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 = 4.285714286 + 4 Reorder the terms: 4 + 4x + x2 = 4.285714286 + 4 Combine like terms: 4.285714286 + 4 = 8.285714286 4 + 4x + x2 = 8.285714286 Factor a perfect square on the left side: (x + 2)(x + 2) = 8.285714286 Calculate the square root of the right side: 2.878491669 Break this problem into two subproblems by setting (x + 2) equal to 2.878491669 and -2.878491669.Subproblem 1
x + 2 = 2.878491669 Simplifying x + 2 = 2.878491669 Reorder the terms: 2 + x = 2.878491669 Solving 2 + x = 2.878491669 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 = 2.878491669 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.878491669 + -2 x = 2.878491669 + -2 Combine like terms: 2.878491669 + -2 = 0.878491669 x = 0.878491669 Simplifying x = 0.878491669Subproblem 2
x + 2 = -2.878491669 Simplifying x + 2 = -2.878491669 Reorder the terms: 2 + x = -2.878491669 Solving 2 + x = -2.878491669 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 = -2.878491669 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.878491669 + -2 x = -2.878491669 + -2 Combine like terms: -2.878491669 + -2 = -4.878491669 x = -4.878491669 Simplifying x = -4.878491669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.878491669, -4.878491669}
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