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Simplifying -12x2 + -2x + -7x2 + 3 + 9x = 0 Reorder the terms: 3 + -2x + 9x + -12x2 + -7x2 = 0 Combine like terms: -2x + 9x = 7x 3 + 7x + -12x2 + -7x2 = 0 Combine like terms: -12x2 + -7x2 = -19x2 3 + 7x + -19x2 = 0 Solving 3 + 7x + -19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.1578947368 + -0.3684210526x + x2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + -0.3684210526x + 0.1578947368 + x2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + -0.3684210526x + x2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + -0.3684210526x + x2 = 0 + 0.1578947368 -0.3684210526x + x2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 -0.3684210526x + x2 = 0.1578947368 The x term is -0.3684210526x. Take half its coefficient (-0.1842105263). Square it (0.03393351800) and add it to both sides. Add '0.03393351800' to each side of the equation. -0.3684210526x + 0.03393351800 + x2 = 0.1578947368 + 0.03393351800 Reorder the terms: 0.03393351800 + -0.3684210526x + x2 = 0.1578947368 + 0.03393351800 Combine like terms: 0.1578947368 + 0.03393351800 = 0.1918282548 0.03393351800 + -0.3684210526x + x2 = 0.1918282548 Factor a perfect square on the left side: (x + -0.1842105263)(x + -0.1842105263) = 0.1918282548 Calculate the square root of the right side: 0.437982026 Break this problem into two subproblems by setting (x + -0.1842105263) equal to 0.437982026 and -0.437982026.Subproblem 1
x + -0.1842105263 = 0.437982026 Simplifying x + -0.1842105263 = 0.437982026 Reorder the terms: -0.1842105263 + x = 0.437982026 Solving -0.1842105263 + x = 0.437982026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1842105263' to each side of the equation. -0.1842105263 + 0.1842105263 + x = 0.437982026 + 0.1842105263 Combine like terms: -0.1842105263 + 0.1842105263 = 0.0000000000 0.0000000000 + x = 0.437982026 + 0.1842105263 x = 0.437982026 + 0.1842105263 Combine like terms: 0.437982026 + 0.1842105263 = 0.6221925523 x = 0.6221925523 Simplifying x = 0.6221925523Subproblem 2
x + -0.1842105263 = -0.437982026 Simplifying x + -0.1842105263 = -0.437982026 Reorder the terms: -0.1842105263 + x = -0.437982026 Solving -0.1842105263 + x = -0.437982026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1842105263' to each side of the equation. -0.1842105263 + 0.1842105263 + x = -0.437982026 + 0.1842105263 Combine like terms: -0.1842105263 + 0.1842105263 = 0.0000000000 0.0000000000 + x = -0.437982026 + 0.1842105263 x = -0.437982026 + 0.1842105263 Combine like terms: -0.437982026 + 0.1842105263 = -0.2537714997 x = -0.2537714997 Simplifying x = -0.2537714997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6221925523, -0.2537714997}
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