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Simplifying 2x * 2x + 6x + -95 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + 6x + -95 = 0 Multiply 2 * 2 4x * x + 6x + -95 = 0 Multiply x * x 4x2 + 6x + -95 = 0 Reorder the terms: -95 + 6x + 4x2 = 0 Solving -95 + 6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -23.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + 1.5x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + 1.5x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + 1.5x + x2 = 0 + 23.75 1.5x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 1.5x + x2 = 23.75 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 23.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 23.75 + 0.5625 Combine like terms: 23.75 + 0.5625 = 24.3125 0.5625 + 1.5x + x2 = 24.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 24.3125 Calculate the square root of the right side: 4.930770731 Break this problem into two subproblems by setting (x + 0.75) equal to 4.930770731 and -4.930770731.Subproblem 1
x + 0.75 = 4.930770731 Simplifying x + 0.75 = 4.930770731 Reorder the terms: 0.75 + x = 4.930770731 Solving 0.75 + x = 4.930770731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.930770731 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.930770731 + -0.75 x = 4.930770731 + -0.75 Combine like terms: 4.930770731 + -0.75 = 4.180770731 x = 4.180770731 Simplifying x = 4.180770731Subproblem 2
x + 0.75 = -4.930770731 Simplifying x + 0.75 = -4.930770731 Reorder the terms: 0.75 + x = -4.930770731 Solving 0.75 + x = -4.930770731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.930770731 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.930770731 + -0.75 x = -4.930770731 + -0.75 Combine like terms: -4.930770731 + -0.75 = -5.680770731 x = -5.680770731 Simplifying x = -5.680770731Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.180770731, -5.680770731}
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