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Simplifying 3x + 7 + -7x * 12x = 4x + 9 Reorder the terms for easier multiplication: 3x + 7 + -7 * 12x * x = 4x + 9 Multiply -7 * 12 3x + 7 + -84x * x = 4x + 9 Multiply x * x 3x + 7 + -84x2 = 4x + 9 Reorder the terms: 7 + 3x + -84x2 = 4x + 9 Reorder the terms: 7 + 3x + -84x2 = 9 + 4x Solving 7 + 3x + -84x2 = 9 + 4x Solving for variable 'x'. Reorder the terms: 7 + -9 + 3x + -4x + -84x2 = 9 + 4x + -9 + -4x Combine like terms: 7 + -9 = -2 -2 + 3x + -4x + -84x2 = 9 + 4x + -9 + -4x Combine like terms: 3x + -4x = -1x -2 + -1x + -84x2 = 9 + 4x + -9 + -4x Reorder the terms: -2 + -1x + -84x2 = 9 + -9 + 4x + -4x Combine like terms: 9 + -9 = 0 -2 + -1x + -84x2 = 0 + 4x + -4x -2 + -1x + -84x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -2 + -1x + -84x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + x + 84x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x + 84x2)' equal to zero and attempt to solve: Simplifying 2 + x + 84x2 = 0 Solving 2 + x + 84x2 = 0 Begin completing the square. Divide all terms by 84 the coefficient of the squared term: Divide each side by '84'. 0.02380952381 + 0.01190476190x + x2 = 0 Move the constant term to the right: Add '-0.02380952381' to each side of the equation. 0.02380952381 + 0.01190476190x + -0.02380952381 + x2 = 0 + -0.02380952381 Reorder the terms: 0.02380952381 + -0.02380952381 + 0.01190476190x + x2 = 0 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + 0.01190476190x + x2 = 0 + -0.02380952381 0.01190476190x + x2 = 0 + -0.02380952381 Combine like terms: 0 + -0.02380952381 = -0.02380952381 0.01190476190x + x2 = -0.02380952381 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01190476190x + 0.25 + x2 = -0.02380952381 + 0.25 Reorder the terms: 0.25 + 0.01190476190x + x2 = -0.02380952381 + 0.25 Combine like terms: -0.02380952381 + 0.25 = 0.22619047619 0.25 + 0.01190476190x + x2 = 0.22619047619 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.22619047619 Calculate the square root of the right side: 0.475594866 Break this problem into two subproblems by setting (x + 0.5) equal to 0.475594866 and -0.475594866.Subproblem 1
x + 0.5 = 0.475594866 Simplifying x + 0.5 = 0.475594866 Reorder the terms: 0.5 + x = 0.475594866 Solving 0.5 + x = 0.475594866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.475594866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.475594866 + -0.5 x = 0.475594866 + -0.5 Combine like terms: 0.475594866 + -0.5 = -0.024405134 x = -0.024405134 Simplifying x = -0.024405134Subproblem 2
x + 0.5 = -0.475594866 Simplifying x + 0.5 = -0.475594866 Reorder the terms: 0.5 + x = -0.475594866 Solving 0.5 + x = -0.475594866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.475594866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.475594866 + -0.5 x = -0.475594866 + -0.5 Combine like terms: -0.475594866 + -0.5 = -0.975594866 x = -0.975594866 Simplifying x = -0.975594866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.024405134, -0.975594866}Solution
x = {-0.024405134, -0.975594866}
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