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Simplifying 15 = 7x2 + -4x Reorder the terms: 15 = -4x + 7x2 Solving 15 = -4x + 7x2 Solving for variable 'x'. Reorder the terms: 15 + 4x + -7x2 = -4x + 4x + 7x2 + -7x2 Combine like terms: -4x + 4x = 0 15 + 4x + -7x2 = 0 + 7x2 + -7x2 15 + 4x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 15 + 4x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.142857143 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -0.5714285714x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -0.5714285714x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 2.142857143 -0.5714285714x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -0.5714285714x + x2 = 2.142857143 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 = 2.142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 2.142857143 + 0.08163265305 Combine like terms: 2.142857143 + 0.08163265305 = 2.22448979605 0.08163265305 + -0.5714285714x + x2 = 2.22448979605 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 2.22448979605 Calculate the square root of the right side: 1.491472358 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.491472358 and -1.491472358.Subproblem 1
x + -0.2857142857 = 1.491472358 Simplifying x + -0.2857142857 = 1.491472358 Reorder the terms: -0.2857142857 + x = 1.491472358 Solving -0.2857142857 + x = 1.491472358 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 = 1.491472358 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.491472358 + 0.2857142857 x = 1.491472358 + 0.2857142857 Combine like terms: 1.491472358 + 0.2857142857 = 1.7771866437 x = 1.7771866437 Simplifying x = 1.7771866437Subproblem 2
x + -0.2857142857 = -1.491472358 Simplifying x + -0.2857142857 = -1.491472358 Reorder the terms: -0.2857142857 + x = -1.491472358 Solving -0.2857142857 + x = -1.491472358 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 = -1.491472358 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.491472358 + 0.2857142857 x = -1.491472358 + 0.2857142857 Combine like terms: -1.491472358 + 0.2857142857 = -1.2057580723 x = -1.2057580723 Simplifying x = -1.2057580723Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7771866437, -1.2057580723}
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