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Simplifying 7x2 + -4x + 392 = 1904 Reorder the terms: 392 + -4x + 7x2 = 1904 Solving 392 + -4x + 7x2 = 1904 Solving for variable 'x'. Reorder the terms: 392 + -1904 + -4x + 7x2 = 1904 + -1904 Combine like terms: 392 + -1904 = -1512 -1512 + -4x + 7x2 = 1904 + -1904 Combine like terms: 1904 + -1904 = 0 -1512 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -216 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '216' to each side of the equation. -216 + -0.5714285714x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + -0.5714285714x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + -0.5714285714x + x2 = 0 + 216 -0.5714285714x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 -0.5714285714x + x2 = 216 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 = 216 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 216 + 0.08163265305 Combine like terms: 216 + 0.08163265305 = 216.08163265305 0.08163265305 + -0.5714285714x + x2 = 216.08163265305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 216.08163265305 Calculate the square root of the right side: 14.699715394 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 14.699715394 and -14.699715394.Subproblem 1
x + -0.2857142857 = 14.699715394 Simplifying x + -0.2857142857 = 14.699715394 Reorder the terms: -0.2857142857 + x = 14.699715394 Solving -0.2857142857 + x = 14.699715394 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 = 14.699715394 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 14.699715394 + 0.2857142857 x = 14.699715394 + 0.2857142857 Combine like terms: 14.699715394 + 0.2857142857 = 14.9854296797 x = 14.9854296797 Simplifying x = 14.9854296797Subproblem 2
x + -0.2857142857 = -14.699715394 Simplifying x + -0.2857142857 = -14.699715394 Reorder the terms: -0.2857142857 + x = -14.699715394 Solving -0.2857142857 + x = -14.699715394 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 = -14.699715394 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -14.699715394 + 0.2857142857 x = -14.699715394 + 0.2857142857 Combine like terms: -14.699715394 + 0.2857142857 = -14.4140011083 x = -14.4140011083 Simplifying x = -14.4140011083Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.9854296797, -14.4140011083}
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