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Simplifying 7x2 + 9x + -4 = 0 Reorder the terms: -4 + 9x + 7x2 = 0 Solving -4 + 9x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 1.285714286x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 1.285714286x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + 0.5714285714 1.285714286x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 1.285714286x + x2 = 0.5714285714 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 0.5714285714 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 0.5714285714 + 0.4132653063 Combine like terms: 0.5714285714 + 0.4132653063 = 0.9846938777 0.4132653063 + 1.285714286x + x2 = 0.9846938777 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.9846938777 Calculate the square root of the right side: 0.992317428 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.992317428 and -0.992317428.Subproblem 1
x + 0.642857143 = 0.992317428 Simplifying x + 0.642857143 = 0.992317428 Reorder the terms: 0.642857143 + x = 0.992317428 Solving 0.642857143 + x = 0.992317428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 0.992317428 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.992317428 + -0.642857143 x = 0.992317428 + -0.642857143 Combine like terms: 0.992317428 + -0.642857143 = 0.349460285 x = 0.349460285 Simplifying x = 0.349460285Subproblem 2
x + 0.642857143 = -0.992317428 Simplifying x + 0.642857143 = -0.992317428 Reorder the terms: 0.642857143 + x = -0.992317428 Solving 0.642857143 + x = -0.992317428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -0.992317428 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.992317428 + -0.642857143 x = -0.992317428 + -0.642857143 Combine like terms: -0.992317428 + -0.642857143 = -1.635174571 x = -1.635174571 Simplifying x = -1.635174571Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.349460285, -1.635174571}
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