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Simplifying 7x2 = 8 + -4x Solving 7x2 = 8 + -4x Solving for variable 'x'. Reorder the terms: -8 + 4x + 7x2 = 8 + -4x + -8 + 4x Reorder the terms: -8 + 4x + 7x2 = 8 + -8 + -4x + 4x Combine like terms: 8 + -8 = 0 -8 + 4x + 7x2 = 0 + -4x + 4x -8 + 4x + 7x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -8 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.5714285714x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.5714285714x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 1.142857143 0.5714285714x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.5714285714x + x2 = 1.142857143 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 1.142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 1.142857143 + 0.08163265305 Combine like terms: 1.142857143 + 0.08163265305 = 1.22448979605 0.08163265305 + 0.5714285714x + x2 = 1.22448979605 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 1.22448979605 Calculate the square root of the right side: 1.10656667 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.10656667 and -1.10656667.Subproblem 1
x + 0.2857142857 = 1.10656667 Simplifying x + 0.2857142857 = 1.10656667 Reorder the terms: 0.2857142857 + x = 1.10656667 Solving 0.2857142857 + x = 1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.10656667 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.10656667 + -0.2857142857 x = 1.10656667 + -0.2857142857 Combine like terms: 1.10656667 + -0.2857142857 = 0.8208523843 x = 0.8208523843 Simplifying x = 0.8208523843Subproblem 2
x + 0.2857142857 = -1.10656667 Simplifying x + 0.2857142857 = -1.10656667 Reorder the terms: 0.2857142857 + x = -1.10656667 Solving 0.2857142857 + x = -1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.10656667 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.10656667 + -0.2857142857 x = -1.10656667 + -0.2857142857 Combine like terms: -1.10656667 + -0.2857142857 = -1.3922809557 x = -1.3922809557 Simplifying x = -1.3922809557Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8208523843, -1.3922809557}
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