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Simplifying 2x + -3 + 6x2(7) = 0 Reorder the terms for easier multiplication: 2x + -3 + 6 * 7x2 = 0 Multiply 6 * 7 2x + -3 + 42x2 = 0 Reorder the terms: -3 + 2x + 42x2 = 0 Solving -3 + 2x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.07142857143 + 0.04761904762x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + 0.04761904762x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + 0.04761904762x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + 0.04761904762x + x2 = 0 + 0.07142857143 0.04761904762x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 0.04761904762x + x2 = 0.07142857143 The x term is 0.04761904762x. Take half its coefficient (0.02380952381). Square it (0.0005668934241) and add it to both sides. Add '0.0005668934241' to each side of the equation. 0.04761904762x + 0.0005668934241 + x2 = 0.07142857143 + 0.0005668934241 Reorder the terms: 0.0005668934241 + 0.04761904762x + x2 = 0.07142857143 + 0.0005668934241 Combine like terms: 0.07142857143 + 0.0005668934241 = 0.0719954648541 0.0005668934241 + 0.04761904762x + x2 = 0.0719954648541 Factor a perfect square on the left side: (x + 0.02380952381)(x + 0.02380952381) = 0.0719954648541 Calculate the square root of the right side: 0.268319706 Break this problem into two subproblems by setting (x + 0.02380952381) equal to 0.268319706 and -0.268319706.Subproblem 1
x + 0.02380952381 = 0.268319706 Simplifying x + 0.02380952381 = 0.268319706 Reorder the terms: 0.02380952381 + x = 0.268319706 Solving 0.02380952381 + x = 0.268319706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02380952381' to each side of the equation. 0.02380952381 + -0.02380952381 + x = 0.268319706 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + x = 0.268319706 + -0.02380952381 x = 0.268319706 + -0.02380952381 Combine like terms: 0.268319706 + -0.02380952381 = 0.24451018219 x = 0.24451018219 Simplifying x = 0.24451018219Subproblem 2
x + 0.02380952381 = -0.268319706 Simplifying x + 0.02380952381 = -0.268319706 Reorder the terms: 0.02380952381 + x = -0.268319706 Solving 0.02380952381 + x = -0.268319706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02380952381' to each side of the equation. 0.02380952381 + -0.02380952381 + x = -0.268319706 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + x = -0.268319706 + -0.02380952381 x = -0.268319706 + -0.02380952381 Combine like terms: -0.268319706 + -0.02380952381 = -0.29212922981 x = -0.29212922981 Simplifying x = -0.29212922981Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24451018219, -0.29212922981}
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