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Simplifying (9x2 + -4x + 10) + (2x2 + 7x + -69) = 0 Reorder the terms: (10 + -4x + 9x2) + (2x2 + 7x + -69) = 0 Remove parenthesis around (10 + -4x + 9x2) 10 + -4x + 9x2 + (2x2 + 7x + -69) = 0 Reorder the terms: 10 + -4x + 9x2 + (-69 + 7x + 2x2) = 0 Remove parenthesis around (-69 + 7x + 2x2) 10 + -4x + 9x2 + -69 + 7x + 2x2 = 0 Reorder the terms: 10 + -69 + -4x + 7x + 9x2 + 2x2 = 0 Combine like terms: 10 + -69 = -59 -59 + -4x + 7x + 9x2 + 2x2 = 0 Combine like terms: -4x + 7x = 3x -59 + 3x + 9x2 + 2x2 = 0 Combine like terms: 9x2 + 2x2 = 11x2 -59 + 3x + 11x2 = 0 Solving -59 + 3x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -5.363636364 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '5.363636364' to each side of the equation. -5.363636364 + 0.2727272727x + 5.363636364 + x2 = 0 + 5.363636364 Reorder the terms: -5.363636364 + 5.363636364 + 0.2727272727x + x2 = 0 + 5.363636364 Combine like terms: -5.363636364 + 5.363636364 = 0.000000000 0.000000000 + 0.2727272727x + x2 = 0 + 5.363636364 0.2727272727x + x2 = 0 + 5.363636364 Combine like terms: 0 + 5.363636364 = 5.363636364 0.2727272727x + x2 = 5.363636364 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 5.363636364 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 5.363636364 + 0.01859504133 Combine like terms: 5.363636364 + 0.01859504133 = 5.38223140533 0.01859504133 + 0.2727272727x + x2 = 5.38223140533 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 5.38223140533 Calculate the square root of the right side: 2.319963665 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 2.319963665 and -2.319963665.Subproblem 1
x + 0.1363636364 = 2.319963665 Simplifying x + 0.1363636364 = 2.319963665 Reorder the terms: 0.1363636364 + x = 2.319963665 Solving 0.1363636364 + x = 2.319963665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 2.319963665 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 2.319963665 + -0.1363636364 x = 2.319963665 + -0.1363636364 Combine like terms: 2.319963665 + -0.1363636364 = 2.1836000286 x = 2.1836000286 Simplifying x = 2.1836000286Subproblem 2
x + 0.1363636364 = -2.319963665 Simplifying x + 0.1363636364 = -2.319963665 Reorder the terms: 0.1363636364 + x = -2.319963665 Solving 0.1363636364 + x = -2.319963665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -2.319963665 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -2.319963665 + -0.1363636364 x = -2.319963665 + -0.1363636364 Combine like terms: -2.319963665 + -0.1363636364 = -2.4563273014 x = -2.4563273014 Simplifying x = -2.4563273014Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1836000286, -2.4563273014}
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