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Simplifying (4x2 + -15x + -21) + (3x2 + -10) = 0 Reorder the terms: (-21 + -15x + 4x2) + (3x2 + -10) = 0 Remove parenthesis around (-21 + -15x + 4x2) -21 + -15x + 4x2 + (3x2 + -10) = 0 Reorder the terms: -21 + -15x + 4x2 + (-10 + 3x2) = 0 Remove parenthesis around (-10 + 3x2) -21 + -15x + 4x2 + -10 + 3x2 = 0 Reorder the terms: -21 + -10 + -15x + 4x2 + 3x2 = 0 Combine like terms: -21 + -10 = -31 -31 + -15x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -31 + -15x + 7x2 = 0 Solving -31 + -15x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.428571429 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '4.428571429' to each side of the equation. -4.428571429 + -2.142857143x + 4.428571429 + x2 = 0 + 4.428571429 Reorder the terms: -4.428571429 + 4.428571429 + -2.142857143x + x2 = 0 + 4.428571429 Combine like terms: -4.428571429 + 4.428571429 = 0.000000000 0.000000000 + -2.142857143x + x2 = 0 + 4.428571429 -2.142857143x + x2 = 0 + 4.428571429 Combine like terms: 0 + 4.428571429 = 4.428571429 -2.142857143x + x2 = 4.428571429 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = 4.428571429 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 4.428571429 + 1.147959185 Combine like terms: 4.428571429 + 1.147959185 = 5.576530614 1.147959185 + -2.142857143x + x2 = 5.576530614 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 5.576530614 Calculate the square root of the right side: 2.361467894 Break this problem into two subproblems by setting (x + -1.071428572) equal to 2.361467894 and -2.361467894.Subproblem 1
x + -1.071428572 = 2.361467894 Simplifying x + -1.071428572 = 2.361467894 Reorder the terms: -1.071428572 + x = 2.361467894 Solving -1.071428572 + x = 2.361467894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 2.361467894 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 2.361467894 + 1.071428572 x = 2.361467894 + 1.071428572 Combine like terms: 2.361467894 + 1.071428572 = 3.432896466 x = 3.432896466 Simplifying x = 3.432896466Subproblem 2
x + -1.071428572 = -2.361467894 Simplifying x + -1.071428572 = -2.361467894 Reorder the terms: -1.071428572 + x = -2.361467894 Solving -1.071428572 + x = -2.361467894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -2.361467894 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -2.361467894 + 1.071428572 x = -2.361467894 + 1.071428572 Combine like terms: -2.361467894 + 1.071428572 = -1.290039322 x = -1.290039322 Simplifying x = -1.290039322Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.432896466, -1.290039322}
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