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Simplifying -9x2 + 4x + 21 = 0 Reorder the terms: 21 + 4x + -9x2 = 0 Solving 21 + 4x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.333333333 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.4444444444x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.4444444444x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 2.333333333 -0.4444444444x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.4444444444x + x2 = 2.333333333 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 2.333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 2.333333333 + 0.04938271604 Combine like terms: 2.333333333 + 0.04938271604 = 2.38271604904 0.04938271604 + -0.4444444444x + x2 = 2.38271604904 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 2.38271604904 Calculate the square root of the right side: 1.543604888 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.543604888 and -1.543604888.Subproblem 1
x + -0.2222222222 = 1.543604888 Simplifying x + -0.2222222222 = 1.543604888 Reorder the terms: -0.2222222222 + x = 1.543604888 Solving -0.2222222222 + x = 1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.543604888 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.543604888 + 0.2222222222 x = 1.543604888 + 0.2222222222 Combine like terms: 1.543604888 + 0.2222222222 = 1.7658271102 x = 1.7658271102 Simplifying x = 1.7658271102Subproblem 2
x + -0.2222222222 = -1.543604888 Simplifying x + -0.2222222222 = -1.543604888 Reorder the terms: -0.2222222222 + x = -1.543604888 Solving -0.2222222222 + x = -1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.543604888 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.543604888 + 0.2222222222 x = -1.543604888 + 0.2222222222 Combine like terms: -1.543604888 + 0.2222222222 = -1.3213826658 x = -1.3213826658 Simplifying x = -1.3213826658Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7658271102, -1.3213826658}
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