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Simplifying 7(x + -2) * 3x = 26 Reorder the terms: 7(-2 + x) * 3x = 26 Reorder the terms for easier multiplication: 7 * 3x(-2 + x) = 26 Multiply 7 * 3 21x(-2 + x) = 26 (-2 * 21x + x * 21x) = 26 (-42x + 21x2) = 26 Solving -42x + 21x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -42x + 21x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -42x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.238095238 + -2x + x2 = 0 Move the constant term to the right: Add '1.238095238' to each side of the equation. -1.238095238 + -2x + 1.238095238 + x2 = 0 + 1.238095238 Reorder the terms: -1.238095238 + 1.238095238 + -2x + x2 = 0 + 1.238095238 Combine like terms: -1.238095238 + 1.238095238 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.238095238 -2x + x2 = 0 + 1.238095238 Combine like terms: 0 + 1.238095238 = 1.238095238 -2x + x2 = 1.238095238 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.238095238 + 1 Reorder the terms: 1 + -2x + x2 = 1.238095238 + 1 Combine like terms: 1.238095238 + 1 = 2.238095238 1 + -2x + x2 = 2.238095238 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.238095238 Calculate the square root of the right side: 1.496026483 Break this problem into two subproblems by setting (x + -1) equal to 1.496026483 and -1.496026483.Subproblem 1
x + -1 = 1.496026483 Simplifying x + -1 = 1.496026483 Reorder the terms: -1 + x = 1.496026483 Solving -1 + x = 1.496026483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.496026483 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.496026483 + 1 x = 1.496026483 + 1 Combine like terms: 1.496026483 + 1 = 2.496026483 x = 2.496026483 Simplifying x = 2.496026483Subproblem 2
x + -1 = -1.496026483 Simplifying x + -1 = -1.496026483 Reorder the terms: -1 + x = -1.496026483 Solving -1 + x = -1.496026483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.496026483 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.496026483 + 1 x = -1.496026483 + 1 Combine like terms: -1.496026483 + 1 = -0.496026483 x = -0.496026483 Simplifying x = -0.496026483Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.496026483, -0.496026483}
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