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Simplifying 6x + 50 = 4x2 + 14x + -15 Reorder the terms: 50 + 6x = 4x2 + 14x + -15 Reorder the terms: 50 + 6x = -15 + 14x + 4x2 Solving 50 + 6x = -15 + 14x + 4x2 Solving for variable 'x'. Reorder the terms: 50 + 15 + 6x + -14x + -4x2 = -15 + 14x + 4x2 + 15 + -14x + -4x2 Combine like terms: 50 + 15 = 65 65 + 6x + -14x + -4x2 = -15 + 14x + 4x2 + 15 + -14x + -4x2 Combine like terms: 6x + -14x = -8x 65 + -8x + -4x2 = -15 + 14x + 4x2 + 15 + -14x + -4x2 Reorder the terms: 65 + -8x + -4x2 = -15 + 15 + 14x + -14x + 4x2 + -4x2 Combine like terms: -15 + 15 = 0 65 + -8x + -4x2 = 0 + 14x + -14x + 4x2 + -4x2 65 + -8x + -4x2 = 14x + -14x + 4x2 + -4x2 Combine like terms: 14x + -14x = 0 65 + -8x + -4x2 = 0 + 4x2 + -4x2 65 + -8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 65 + -8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -16.25 + 2x + x2 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + 2x + 16.25 + x2 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + 2x + x2 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + 2x + x2 = 0 + 16.25 2x + x2 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 2x + x2 = 16.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16.25 + 1 Reorder the terms: 1 + 2x + x2 = 16.25 + 1 Combine like terms: 16.25 + 1 = 17.25 1 + 2x + x2 = 17.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 1) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 1 = 4.153311931 Simplifying x + 1 = 4.153311931 Reorder the terms: 1 + x = 4.153311931 Solving 1 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.153311931 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.153311931 + -1 x = 4.153311931 + -1 Combine like terms: 4.153311931 + -1 = 3.153311931 x = 3.153311931 Simplifying x = 3.153311931Subproblem 2
x + 1 = -4.153311931 Simplifying x + 1 = -4.153311931 Reorder the terms: 1 + x = -4.153311931 Solving 1 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.153311931 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.153311931 + -1 x = -4.153311931 + -1 Combine like terms: -4.153311931 + -1 = -5.153311931 x = -5.153311931 Simplifying x = -5.153311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.153311931, -5.153311931}
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