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Simplifying 16 + -7x(2 + 3x) = 0 16 + (2 * -7x + 3x * -7x) = 0 16 + (-14x + -21x2) = 0 Solving 16 + -14x + -21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.7619047619 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.7619047619' to each side of the equation. -0.7619047619 + 0.6666666667x + 0.7619047619 + x2 = 0 + 0.7619047619 Reorder the terms: -0.7619047619 + 0.7619047619 + 0.6666666667x + x2 = 0 + 0.7619047619 Combine like terms: -0.7619047619 + 0.7619047619 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.7619047619 0.6666666667x + x2 = 0 + 0.7619047619 Combine like terms: 0 + 0.7619047619 = 0.7619047619 0.6666666667x + x2 = 0.7619047619 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.7619047619 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.7619047619 + 0.1111111112 Combine like terms: 0.7619047619 + 0.1111111112 = 0.8730158731 0.1111111112 + 0.6666666667x + x2 = 0.8730158731 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.8730158731 Calculate the square root of the right side: 0.934353184 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.934353184 and -0.934353184.Subproblem 1
x + 0.3333333334 = 0.934353184 Simplifying x + 0.3333333334 = 0.934353184 Reorder the terms: 0.3333333334 + x = 0.934353184 Solving 0.3333333334 + x = 0.934353184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.934353184 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.934353184 + -0.3333333334 x = 0.934353184 + -0.3333333334 Combine like terms: 0.934353184 + -0.3333333334 = 0.6010198506 x = 0.6010198506 Simplifying x = 0.6010198506Subproblem 2
x + 0.3333333334 = -0.934353184 Simplifying x + 0.3333333334 = -0.934353184 Reorder the terms: 0.3333333334 + x = -0.934353184 Solving 0.3333333334 + x = -0.934353184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.934353184 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.934353184 + -0.3333333334 x = -0.934353184 + -0.3333333334 Combine like terms: -0.934353184 + -0.3333333334 = -1.2676865174 x = -1.2676865174 Simplifying x = -1.2676865174Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6010198506, -1.2676865174}
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