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Simplifying 7x * 7x + 9x + -66 = 0 Reorder the terms for easier multiplication: 7 * 7x * x + 9x + -66 = 0 Multiply 7 * 7 49x * x + 9x + -66 = 0 Multiply x * x 49x2 + 9x + -66 = 0 Reorder the terms: -66 + 9x + 49x2 = 0 Solving -66 + 9x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.346938776 + 0.1836734694x + x2 = 0 Move the constant term to the right: Add '1.346938776' to each side of the equation. -1.346938776 + 0.1836734694x + 1.346938776 + x2 = 0 + 1.346938776 Reorder the terms: -1.346938776 + 1.346938776 + 0.1836734694x + x2 = 0 + 1.346938776 Combine like terms: -1.346938776 + 1.346938776 = 0.000000000 0.000000000 + 0.1836734694x + x2 = 0 + 1.346938776 0.1836734694x + x2 = 0 + 1.346938776 Combine like terms: 0 + 1.346938776 = 1.346938776 0.1836734694x + x2 = 1.346938776 The x term is 0.1836734694x. Take half its coefficient (0.0918367347). Square it (0.008433985840) and add it to both sides. Add '0.008433985840' to each side of the equation. 0.1836734694x + 0.008433985840 + x2 = 1.346938776 + 0.008433985840 Reorder the terms: 0.008433985840 + 0.1836734694x + x2 = 1.346938776 + 0.008433985840 Combine like terms: 1.346938776 + 0.008433985840 = 1.35537276184 0.008433985840 + 0.1836734694x + x2 = 1.35537276184 Factor a perfect square on the left side: (x + 0.0918367347)(x + 0.0918367347) = 1.35537276184 Calculate the square root of the right side: 1.164204777 Break this problem into two subproblems by setting (x + 0.0918367347) equal to 1.164204777 and -1.164204777.Subproblem 1
x + 0.0918367347 = 1.164204777 Simplifying x + 0.0918367347 = 1.164204777 Reorder the terms: 0.0918367347 + x = 1.164204777 Solving 0.0918367347 + x = 1.164204777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0918367347' to each side of the equation. 0.0918367347 + -0.0918367347 + x = 1.164204777 + -0.0918367347 Combine like terms: 0.0918367347 + -0.0918367347 = 0.0000000000 0.0000000000 + x = 1.164204777 + -0.0918367347 x = 1.164204777 + -0.0918367347 Combine like terms: 1.164204777 + -0.0918367347 = 1.0723680423 x = 1.0723680423 Simplifying x = 1.0723680423Subproblem 2
x + 0.0918367347 = -1.164204777 Simplifying x + 0.0918367347 = -1.164204777 Reorder the terms: 0.0918367347 + x = -1.164204777 Solving 0.0918367347 + x = -1.164204777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0918367347' to each side of the equation. 0.0918367347 + -0.0918367347 + x = -1.164204777 + -0.0918367347 Combine like terms: 0.0918367347 + -0.0918367347 = 0.0000000000 0.0000000000 + x = -1.164204777 + -0.0918367347 x = -1.164204777 + -0.0918367347 Combine like terms: -1.164204777 + -0.0918367347 = -1.2560415117 x = -1.2560415117 Simplifying x = -1.2560415117Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0723680423, -1.2560415117}
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